This standard may only be used by approved subscription and freemailing clients of the SABS.
ICS 91.080.40
SABS 0100-1*
ISBN 0-626-12497-2
*This standard references other standards
Edition 2.2
2000
SOUTH AFRICAN STANDARD Code of practice
The structural use of concrete Part 1: Design
Consolidated edition incorporating amendment No. 1 : 11 April 1994 technical corrigendum No. 1 : 26 September 1994 amendment No. 2 : 31 March 2000
Published by THE SOUTH AFRICAN BUREAU OF STANDARDS
Gr 20
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
Amendments issued since publication Amdt No.
Date
Text affected
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
ICS 91.080.40
SOUTH AFRICAN BUREAU OF STANDARDS CODE OF PRACTICE
THE STRUCTURAL USE OF CONCRETE PART 1: DESIGN
Obtainable from the South African Bureau of Standards Private Bag X191 Pretoria Republic of South Africa 0001 Telephone Fax E-mail Website
: (012) 428-7911 : (012) 344-1568 :
[email protected] : http://www.sabs.co.za
COPYRIGHT RESERVED Printed in the Republic of South Africa by the South African Bureau of Standards
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
Notice | |
This part of SABS 0100 was approved in accordance with SABS procedures on 13 August 1992. Amendment No. 2 was approved in accordance with SABS procedures on 31 March 2000. Amdt 2, March 2000 NOTE 1 In terms of the Standards Act, 1993 (Act 29 of 1993), no person shall claim or declare that he or any other person complied with an SABS standard unless a) such claim or declaration is true and accurate in all material respects, and b) the identity of the person on whose authority such claim or declaration is made, is clear. NOTE 2 It is recommended that authorities who wish to incorporate any part of this standard into any legislation in the manner intended by section 31 of the Act consult the SABS regarding the implications.
This part of SABS 0100 will be revised when necessary in order to keep abreast of progress. Comment will be welcome and will be considered when this part of SABS 0100 is revised.
Foreword |
Edition 2.2 cancels and replaces all previous editions
Amdt 2, March 2000
Annex A (Methods of checking for compliance with serviceability criteria by direct calculation), annex B (Movement joints), annex C (Elastic deformation of concrete), annex D (The design of deep beams) and annex E (Bibliography) are for information only. SABS 0100 consists of the following parts, under the general title The structural use of concrete: - Part 1: Design - Part 2: Materials and workmanship A vertical line in the margin shows where the text has been modified by amendment Nos. 1 and 2.
Introduction The Council of the South African Bureau of Standards decided that the South African code of practice for the structural use of concrete should be based on the British Standards Institution codes of practice BS 8110-1:1985 and BS 8110-2:1985. It should be emphasized, however, that the South African code uses different loading procedures (compatible with section 4 of SABS 0160:1989) and introduces a few minor changes on account of South African conditions.
Attention is drawn to the normative references given in clause 2 of this standard. These references are indispensable for the application of this standard.
ISBN 0-626-12497-2
ii
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
Contents Page Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1
Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2
Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3
Limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6
4
General objectives and recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Limit states requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Ultimate limit state (ULS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Serviceability limit states (SLS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Loads and strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Values for the ultimate limit state (loads and materials) . . . . . . . . . . . . . . . . . . . . . . . 8 Values for serviceability limit states (loads and materials) . . . . . . . . . . . . . . . . . . . . . 9 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Properties of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Analysis (ultimate limit state) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Analysis (serviceability limit states) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Model analysis and testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Experimental development of analytical procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Reinforced concrete (design and detailing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.3 4.3.1 4.3.2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Basis of limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Analysis of structures and structural frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Analysis of complete structures and complete structural frames . . . . . . . . . . . . . . . . 17 Analysis of structural frames supporting vertical loads only . . . . . . . . . . . . . . . . . . . . 17 Analysis of structural frames supporting vertical and lateral loads . . . . . . . . . . . . . . . 18 Redistribution of moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Column and beam construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
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This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 4.3.3 4.3.4 4.3.5 4.3.6 4.3.7 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.4.7 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.5.7 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 4.7.6 4.7.7 4.8 4.8.1 4.8.2 4.8.3 4.8.4 4.8.5 4.8.6 4.8.7 4.9 4.9.1 4.9.2 4.10 4.10.1 4.10.2 4.10.3 4.10.4 4.11 4.11.1 4.11.2
iv
Moments of resistance at ultimate limit state for beams . . . . . . . . . . . . . . . . . . . . . . . 22 Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Crack control in beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Design of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Moments and forces in solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 One-way spanning slabs of approximately equal span . . . . . . . . . . . . . . . . . . . . . . 42 Solid slabs spanning in two directions at right angles (uniformly distributed loads) 43 Shear resistance of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Deflection of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Crack control in solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Ribbed slabs (with solid or hollow blocks or with voids) . . . . . . . . . . . . . . . . . . . . . 55 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Analysis of structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Moments of resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Arrangement of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Flat slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Shear in flat slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Deflection of panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Crack control in panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Analysis and design of flat slab structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Moments and forces in columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Moments induced by deflection in solid slender columns . . . . . . . . . . . . . . . . . . . . 76 Design of column section for ULS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Deflection of columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Crack control in columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Special creep and shrinkage conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Reinforced concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 General definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Structural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Forces and moments in reinforced concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Short reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Slender reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Deflection of reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Crack control in reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Staircases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Design of staircases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Moments and forces in bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Design of pad footings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Design of pile caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Considerations affecting design details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Constructional deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Concrete cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 4.11.3 4.11.4 4.11.5 4.11.6 4.11.7 4.11.8 4.11.9 4.12 4.12.1 4.12.2 4.12.3 4.12.4 4.12.5 4.12.6 4.12.7 4.12.8 4.12.9 4.12.10 4.12.11 4.12.12 5
Reinforcement (general considerations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum areas of reinforcement in elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum areas of reinforcement in element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bond, anchorage, bearing, laps, joints and bends in bars . . . . . . . . . . . . . . . . . . . Curtailment and anchorage of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spacing of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional considerations when low density aggregate concrete is used . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear resistance of slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deflection of slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local bond, anchorage bond and laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bearing stress inside bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92 93 96 96 101 106 108 110 110 110 110 110 111 111 111 112 112 112 112 112
Prestressed concrete (design and detailing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.4 5.5 5.6 5.7 5.8 5.8.1 5.8.2 5.8.3 5.8.4 5.8.5 5.9 5.9.1 5.9.2 5.9.3 5.9.4
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basis of design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability and other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structures and structural frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Redistribution of moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Serviceability limit state (cracking) for beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultimate limit state for beams in flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tension members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low density aggregate prestressed concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prestressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum initial prestress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loss of prestress other than frictional losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loss of prestress due to friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transmission length in pre-tensioned elements . . . . . . . . . . . . . . . . . . . . . . . . . . . End blocks in prestressed elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Considerations affecting design details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Size and number of prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cover to prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spacing of prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113 113 113 113 113 114 114 114 114 115 115 116 118 122 125 126 126 126 126 126 127 127 127 130 132 133 135 135 135 135 137
v
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 5.9.5 5.9.6 5.9.7 5.9.8 6
137 139 140 140
Precast, composite and plain concrete constructions (design and detailing) . . . . . . . . . . . . 140 6.1 6.1.1 6.1.2 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.5 6.5.1 6.5.2 6.5.3
7
Curved tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Longitudinal reinforcement in prestressed concrete beams . . . . . . . . . . . . . . . . . . Links in prestressed concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shock loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Precast concrete construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Framed structures and continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bearings for precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joints between precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structural connections between units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuity of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Connections with structural steel inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other types of connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Composite concrete construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultimate limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thickness of structural topping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design of plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140 140 140 142 142 142 143 143 147 150 150 152 153 153 154 154 154 154 156 158 158 158 158 158
Fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.1 7.2 7.3 7.4 7.5 7.6 7.6.1 7.6.2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional protection to floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concrete walls containing at least 1,0 % of vertical reinforcement . . . . . . . . . . . . . Plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
162 164 169 169 170 172 172 172
Annexes A
Methods of checking for compliance with serviceability criteria by direct calculation . . . . . . 173 A.1 Analysis of structure for serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 A.2 Calculation of deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 A.3 Calculation of crack width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
B
Movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 B.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
vi
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 B.2 B.3 B.4 B.5 C
Need for movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Types of movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Provision of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Design of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Elastic deformation of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 C.1 Modulus of elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 C.2 Creep and shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 C.3 Drying shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
D
The design of deep beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 D.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 D.2 Design and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
E
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Tables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Values for modulus of elasticity of concrete, Ec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Strength of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Characteristic strength of reinforcement, fy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Ultimate bending moments and shear forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Values of the factor βf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Maximum design shear stress vc for grade 25 concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Values of coefficient β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Minimum and ultimate torsional shear stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Reinforcement for shear and torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Basic span/effective depth ratios for rectangular beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Modification factors for tension reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Modification factors for compression reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Ultimate bending moments and shear forces in one-way spanning slabs . . . . . . . . . . . . . . 42 Bending moment coefficients for slabs spanning in two directions at right angles, simply supported on four sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Bending moment coefficients for rectangular panels supported on four sides with provision for torsional reinforcement at the corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Bending moments and shear force coefficients for flat slabs of three or more equal spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Distribution of moments in panels of flat slabs designed as continuous frames . . . . . . . . . . 68 Values of β for braced columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Values of β for unbraced columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Values of βa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Values of coefficient βb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Bar schedule dimensions: deductions for tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Minimum percentage of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Ultimate anchorage bond stress fbu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Maximum clear distance between bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Maximum design shear stress vc in low density aggregate concrete beams . . . . . . . . . . . . 111 Minimum and ultimate torsional shear stress in low density aggregate concrete beams . . . 111 Strength of concrete fcu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Compressive stresses fcu in concrete for serviceability limit states . . . . . . . . . . . . . . . . . . . . 116 Flexural tensile stresses for class 2 elements (serviceability limit state (cracking)) . . . . . . . 117 Depth factors for tensile stresses for class 3 elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
vii
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 32 Conditions at the ultimate limit state for rectangular beams with pre-tensioned tendons or with post-tensioned tendons having an effective bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 33 Conditions at the ultimate limit state for post-tensioned rectangular beams having unbonded tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 34 Values of Vco /bh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 35 Shrinkage of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 36 Transmission lengths for small diameter strand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 37 Design bursting tensile forces in end blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 38 Nominal cover to all steel to meet specified periods of fire resistance . . . . . . . . . . . . . . . . . 136 39 Minimum cover to curved ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 40 Minimum distance between centre-lines of ducts in plane of curvature . . . . . . . . . . . . . . . . 139 41 Deleted by amendment No. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 42 Design ultimate horizontal shear stresses at interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 43 Fire resistance of reinforced concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 44 Fire resistance of prestressed concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 45 Fire resistance of reinforced concrete floors (siliceous or calcareous aggregate) . . . . . . . . 167 46 Fire resistance of prestressed concrete floors (siliceous or calcareous aggregate) . . . . . . . 168 47 Effect of soffit treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 48 Fire resistance of concrete columns (all faces exposed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 49 Fire resistance of concrete columns (one face exposed) . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 50 Fire resistance of siliceous aggregate concrete walls containing at least 1,0 % of vertical reinforcement and exposed to fire on one face only . . . . . . . . . . . . . . . . . . 172 C.1 Modulus of elasticity of normal-density concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
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Short-term design stress strain curve for normal density concrete . . . . . . . . . . . . . . . . . . . . 13 Short-term design stress strain curve for reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Short-term design stress strain curve for prestressing reinforcement . . . . . . . . . . . . . . . . . . 14 Ultimate forces, stresses and strains in reinforced concrete sections at the ultimate limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Single system of bent-up bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Shear failure near supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Definition of panels and bays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Effective width of solid slab carrying a concentrated load near an unsupported edge . . . . . 42 Division of slab into middle and edge strips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Apportionment of load for determining the bearing reactions . . . . . . . . . . . . . . . . . . . . . . . . 48 Definition of a shear perimeter for typical cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Punching shear zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Openings in slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Shear perimeters with loads close to free edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Types of column heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Division of flat slab panels into columns and middle strips . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Sections of shear check for flat slabs with drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Shear at slab internal column connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Definition of breadth of effective moment transfer strip be for various typical cases . . . . . . . 69 Effective length charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Braced slender columns - Bending moments chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Unbraced slender columns - Bending moments chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Critical section of shear check in a pile cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Simplified detailing rules for beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Simplified detailing rules for slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Determination of le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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SABS 0100-1 Ed. 2.2 27 Schematic arrangement of allowance for bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.1 Assumptions made in calculating curvatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 A.2 Values of K for various bending moment diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 C.1 Effects of relative humidity, age of concrete at loading and section thickness upon creep factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 C.2 Drying shrinkage of normal-density concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 D.1 Equivalent truss resisting point loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 D.2 Equivalent arch resisting UD load and self-weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 D.3 Equivalent truss resisting unequal point loads A > B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 D.4 Loaded area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
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SABS 0100-1 Ed. 2.2
Committee South African Bureau of Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VJ Woodlock (Chairman) I Jablonski (Standards writer) E Coetzee (Committee clerk)
CSIR Division of Building Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
BG Lunt
Concrete Society of Southern Africa
A Jones
............................
Department of Public Works and Land Affairs . . . . . . . . . . . . . . . . . . . . .
DA Payne
Portland Cement Institute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
JM Clifford
South African Federation of Civil Engineering Contractors . . . . . . . . . . .
HH Meier
The South African Association of Consulting Engineers . . . . . . . . . . . . .
GJ de Ridder
The South African Institution of Civil Engineers . . . . . . . . . . . . . . . . . . . .
AE Goldstein PC Pretorius H Scholz
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CODE OF PRACTICE
SABS 0100-1 Edition 2.2
The structural use of concrete Part 1: Design
1 Scope 1.1 This part of SABS 0100 establishes principles for the structural use of concrete under the following stipulations: a) method of design: limit states classified as ultimate limit state and serviceability limit states; b) material: ordinary concrete of normal and low density, used in reinforced, prestressed and precast structures or elements and in plain concrete walls; c) types of structures: buildings and structures in which all load-bearing elements (e.g. slabs, columns, walls, etc.) are of concrete. NOTE -The rules for stability (see clause 3) also apply to structures in which concrete elements such as floor slabs and walls are used in conjunction with load-bearing elements made of other materials.
1.2 This part of SABS 0100 does not cover the structural use of concrete for structures that are the subject of specialist literature (shells, folded plates, bridges, tunnels, retaining walls, water-retaining structures, chimneys, and other specialized elements).
2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this part of SABS 0100. All standards are subject to revision and, since any reference to a standard is deemed to be a reference to the latest edition of that standard, parties to agreements based on this part of SABS 0100 are encouraged to take steps to ensure the use of the most recent editions of the standards indicated below. Information on currently valid national and international standards may be obtained from the South African Bureau of Standards. SABS 82, Bending dimensions and scheduling of steel reinforcement for concrete. |
Reference deleted by amendment No. 1.
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SABS 0100-1 Ed. 2.2 SABS 920, Steel bars for concrete reinforcement. SABS 0100-2, The structural use of concrete - Part 2: Materials and execution of work. SABS 0144, Detailing of steel reinforcement for concrete. SABS 0160 (as amended), The general procedures and loadings to be adopted in the design of buildings.
3 Limit states design 3.1 General objectives and recommendations The objective of design by the limit states method is to achieve reasonable probabilities that the structure being designed will not reach a limit state (i.e. will not become unfit for use) and that the structure will be durable. To achieve this objective, the factors given below should be taken into consideration.
3.1.1 The characteristic values of strengths and the nominal values of loads should be considered in the initial stages of design, in order to take into account the variations in the strengths and properties of the materials to be used and the variations in the loads to be supported. Where the necessary data are available, the values should be based on statistical evidence (characteristic values) and where the data are not available, the values should be based on an appraisal of experience (nominal values).
3.1.2 Two sorts of partial safety factors are to be used, one for material strength and the other for loads. In the absence of special considerations, these partial safety factors should have the values given in 3.3, appropriate to the limit state being considered, the type of loading and the material being used.
3.2 Limit states requirements 3.2.1 General All relevant limit states should be considered in the initial stages of the design so as to ensure an adequate degree of safety and serviceability. The general rule, however, will be to design on the basis of the expected critical limit state and then to check that the remaining limit states will not be reached.
3.2.2 Ultimate limit state (ULS) 3.2.2.1 General Ultimate limit states are those concerning safety, and they correspond to the maximum load-carrying capacity of a structure. An ultimate limit state is reached when the structure is not strong enough to withstand the design loads, i.e. when the resistance of a critical section (or sections) to compression, tension, shear or torsion is insufficient. This will result in loss of equilibrium of the whole or of a part of the structure regarded as a rigid body, with the following symptoms being likely to occur: a) the rupture of one or more critical sections (due to overloading, fatigue, fire or deformation); b) overturning or buckling caused by elastic or plastic instability, sway, wind flutter or ponding; and c) very large deformation, e.g. transformation of the structure into a mechanism.
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SABS 0100-1 Ed. 2.2 3.2.2.2 Stability Structures should be so designed that adequate means exist to transmit the design ultimate self-weight load, wind load and imposed loads safely from the highest supported level to the foundations. The layout of the structure and the interaction between the structural elements should be such as to ensure a stable design. The engineer responsible for the overall stability of the structure should ensure the compatibility of the design and details of parts and components, even where all or part of the design and details thereof were undertaken by someone else. 3.2.2.3 Robustness Structures should be so designed that they are not unreasonably susceptible to the effects of accidents. In particular, situations should be avoided where damage to a small area of a structure or failure of a single element could lead to the collapse of major sections of the structure. In general, if any failure were to occur, it should be in the beams and not in the columns. Unreasonable susceptibility to the effects of accidents may generally be prevented if the factors given below are taken into consideration. 3.2.2.3.1 Structures should be capable of safely resisting the design ultimate horizontal load, as given in 4.1.2, applied at each floor or roof level simultaneously. 3.2.2.3.2 Structures should have effective horizontal ties (see 4.11.9) a) around the periphery, b) internally, and c) to columns and walls. 3.2.2.3.3 The layout of buildings of five storeys or more should be checked to identify any key elements whose failure would cause the collapse of more than a limited portion close to these key elements. Where such elements are identified and the layout cannot be revised to avoid them, the design should take their importance into account. The likely consequences of a failure of a key element should be considered when appropriate design loads are chosen. In all cases, an element and its connections should be capable of withstanding a design ultimate load of 34 kN/m2 (to which no partial safety factor should be applied) from any direction. The area to which this load is applied will be the projected area of the element (i.e. the area of the face presented to the load). A horizontal element, or part of a horizontal element that provides lateral supports vital to the stability of a vertical key element, should also be considered a key element. 3.2.2.3.4 Buildings of five storeys or more should be so detailed that any vertical load-bearing element other than a key element can be removed without causing the collapse of more than a limited portion close to that element. This is generally achieved by providing vertical ties (see 4.11.9) in addition to satisfying 3.2.2.3.1 to 3.2.2.3.3. There may, however, be cases where it is inappropriate or impossible to provide effective vertical ties in all or even in some of the vertical load-bearing elements. When this occurs, the removal of each such load-bearing element should be considered, in turn, and the elements normally supported by such load-bearing element should be designed to "bridge" the gap, possibly with the use of catenary action or non-linear deflection effects, and allowing for considerable deflection. 3.2.2.4 Special hazards In designing a structure to support loads occurring in the course of normal function, ensure that there
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SABS 0100-1 Ed. 2.2 is a reasonable probability that the structure will not collapse disastrously as a result of misuse or accident. Consider whether, due to the nature of a particular occupancy or use of a structure (e.g. flour mill, chemical plant, etc.), it will be necessary in the design concept or during a design reappraisal to consider the effect of a particular hazard, to ensure that, in the event of an accident, there is a reasonable probability that the structure will withstand the accident, even if damage does occur. In such cases, partial safety factors greater than those given in 3.3.1.2 may be required. NOTE - No structure can be expected to withstand the excessive loads or forces that could arise owing to an extreme cause (such as an explosion), but the structure should not be damaged to an extent that is disproportionate to the original cause.
3.2.2.5 Loads and strength of materials Use the design strength of materials and the design loads appropriate for the ultimate limit state (see 3.3).
3.2.3 Serviceability limit states (SLS) 3.2.3.1 General Serviceability limit states are those that restrict a) excessive deformation (deflection, rotation); b) excessive local damage (cracking, splitting, spalling); c) excessive displacement (slip of connections); d) excessive vibration; and e) corrosion. The above effects are likely to impair the normal use, occupancy, appearance or durability of the structure or of its structural or non-structural elements, or they might affect the operation of equipment. Effects such as temperature, creep, shrinkage, sway, settlement, and cyclic loading should be considered, when relevant. The design strength of materials and the design loads appropriate for serviceability limit states should be used (see 3.3). 3.2.3.2 Deflection 3.2.3.2.1 The deflection of the structure or of any part thereof should not exceed the permissible value. Permissible values of deflection should comply with the requirements of the particular structure, taking the efficient functioning of the structure, possible damage to adjacent structures or aesthetic considerations into account. As a guide, the limits given below can be regarded as reasonable. 3.2.3.2.1.1 The final deflection (including the effects of temperature, creep and shrinkage), measured below the as-cast level of the support of floors, roofs and all other horizontal members, should not exceed span/250.
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SABS 0100-1 Ed. 2.2 3.2.3.2.1.2 Partitions and finishes will be affected only by that part of the deflection (including the effects of temperature, creep and shrinkage) that takes place after the construction of the partitions or the application of the finishes. Information is lacking, but it is suggested that such deflection in the case of flexible partitions (e.g. dry-wall) be limited to the lesser of span/350 or 20 mm. In the case of rigid brick walls or other brittle partitions, this deflection should be limited to the lesser of span/500 or 10 mm. Investigation is required in more complicated cases. 3.2.3.2.1.3 If finishes are to be applied to prestressed concrete elements, the total upward deflection of the elements should not exceed span/300, unless uniformity of camber between adjacent elements can be ensured. 3.2.3.2.2 Consider the effects of lateral deflections, particularly for tall slender structures. The acceleration associated with the deflections may be more critical than the deflection itself (see 3.2.3.4). 3.2.3.2.3 In any calculation of deflections, take the design strength of materials and the design loads given in 3.3, as appropriate for a serviceability limit state. 3.2.3.3 Cracking 3.2.3.3.1 The permissible width of cracks should be determined taking into account the requirements (e.g. tightness, aesthetic appearance, etc.) of the particular structure. As a guide, the limits given below can be regarded as reasonable. 3.2.3.3.1.1 Reinforced concrete An assessment of the likely behaviour of a reinforced concrete structure enables identification of the sections where the effect of cracking should be considered. In general, the surface width of cracks should not exceed 0,3 mm. Where elements are exposed to particularly aggressive environments (see SABS 0100-2), the surface width of cracks at points nearest the main reinforcement should not, in general, exceed 0,004 times the nominal cover to the main reinforcement. In a reinforced concrete structure under the effects of load and environment, the actual widths of cracks will vary considerably; the prediction of an absolute maximum width is therefore not possible, since the possibility of some cracks being even wider must be accepted unless special precautions are taken. 3.2.3.3.1.2 Prestressed concrete In the assessment of the likely behaviour of a prestressed concrete structure, the flexural tensile stress for structures of different classes should be limited as follows: - class 1: no tensile stresses; - class 2: tensile stresses, but no visible cracking; and - class 3: tensile stresses, but surface width of cracks do not exceed 0,1 mm for elements exposed to a particularly aggressive environment (see SABS 0100-2) and do not exceed 0,2 mm for all other elements. 3.2.3.3.2 In either tall or long buildings, the effects of temperature, creep and shrinkage could, unless otherwise catered for, require the provision of movement joints both within the structure and between the structure and the cladding. 3.2.3.3.3 In any calculations of crack widths (see annex A), take the design strength of the materials and the design loads given in 3.3, as appropriate for a serviceability limit state.
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SABS 0100-1 Ed. 2.2 3.2.3.3.4 Sufficient non-prestressed reinforcement should be provided to control cracking adequately. 3.2.3.4 Vibration Where a structure is likely to be subjected to vibration from causes such as wind forces or machinery, take measures to prevent discomfort or alarm, damage to the structure, or interference with its proper function. (Limits to the level of vibration that may be acceptable are described in specialist literature.) NOTE - In certain circumstances, it could be necessary to isolate the source of vibration or, alternatively, to isolate a part or the whole of the structure. Special consideration could be necessary for flexible elements of structure.
3.2.3.5 Other serviceability limit states Ensure that structures designed for unusual or special functions comply with any relevant additional limit states considered necessary by the engineer.
3.2.4 Other considerations 3.2.4.1 Fatigue When the imposed load on a structure is predominantly cyclic in character, take the effects of fatigue into consideration in satisfying limit state requirements. 3.2.4.2 Durability The recommendations in this part of SABS 0100 regarding concrete cover to the reinforcement and acceptable crack widths (see 3.2.3.3) in association with the cement content and cement/water ratios specified in SABS 0100-2, are intended to meet the durability requirements of almost all structures. Where exceptionally severe environments are encountered, consider any additional precautions that may be necessary and consult specialist literature with respect to each particular environment. 3.2.4.3 Fire resistance Consider the following three conditions for structural elements that may be subjected to fire: a) retention of structural strength; b) resistance to penetration of flames; and c) resistance to heat transmission. NOTE - The minimum requirements for different elements for various periods of fire resistance are given in clause 7.
3.2.4.4 Lightning Reinforcement may be used as part of a lightning protection system, but safeguards such as the provision of bonding and the use of a resistance check after the completion of the building are required.
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SABS 0100-1 Ed. 2.2 3.3 Loads and strength of materials 3.3.1 Loads 3.3.1.1 Nominal load The following nominal loads should be used in the design of a structure: a) nominal self-weight load Gn (i.e the weight of the structure complete with finishes, fixtures and partitions); b) nominal imposed load Qn; c) nominal wind load Wn; and d) earth and water pressure. The nominal load values should be taken as defined in and calculated in accordance with SABS 0160. 3.3.1.2 Partial safety factors for load γf The design load for a given type of limit state and loading is obtained from: - Gn.γf = design self-weight load, - Qn.γf = design imposed load, -
Wn.γf = design wind load,
where γf is the appropriate partial safety factor for load, which is introduced to take account of a) possible unusual increases in load beyond those considered in the derivation of the nominal loads, b) inaccurate assessment of the effects of loading, c) unforeseen stress redistribution within the structure, d) the variations in dimensional accuracy achieved in construction, and e) the importance of the limit state that is being considered. 3.3.1.3 Load during construction The loading conditions during erection and construction should be considered in design and should be such that the structure's subsequent compliance with the limit state requirements is not impaired.
3.3.2 Strength of materials 3.3.2.1 Characteristic strength of materials Unless otherwise stated, the characteristic strength of materials means a) the cube strength of concrete fcu,
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SABS 0100-1 Ed. 2.2 b) the yield or proof stress of reinforcement fy, and c) the ultimate strength of a prestressing tendon fpu below which not more than 5 % of the test results fall. 3.3.2.2 Partial safety factors for strength of materials γm For the analysis of sections, the design strength for a given material and limit state is derived from the characteristic strength divided by γm, where γm is the appropriate partial safety factor for material strength given in 3.3.3 and 3.3.4. Factor γm takes account of a) differences between actual and laboratory values of strength, b) local weakness, c) inaccuracies in the assessment of the resistance of sections, and d) the importance of the limit state that is being considered.
3.3.3 Values for the ultimate limit state (loads and materials) 3.3.3.1 Design loads 3.3.3.1.1 Take the design loads for the ultimate limit state (referred to in clauses 4 and 5 as the ultimate loads) in accordance with clause 4 of SABS 0160 (as amended). 3.3.3.1.2 The design load effect may be adjusted, at the discretion of the designer, by multiplying the design load as in 3.3.3.1.1 by an importance factor γc to allow for the consequences of failure. In the case of critical structural elements for structures in which large crowds gather and where there would be very serious consequences in the event of a failure, a value of γc in the range 1,1 to 1,2 should be used. For structures with a very low degree of hazard to life and with less serious consequences of failure, a value of γc of 0,9 would be appropriate. 3.3.3.1.3 In assessing the effect of loads on the whole structure or on any part of the structure, so arrange the loads as to cause the most severe stresses. It will only be necessary to use the factor 0,9 if the self-weight load is an essential factor in the stability, e.g. for cantilevers or for wind forces. If a critical stability condition results in the case of self-weight and wind loads combined and when (on selected parts of the structure) the self-weight load is increased, adopt the higher figure for the self-weight load, i.e. 1,2 Gn. Generally, in the case of self-weight, imposed and wind loads combined, assume that no variations in γf factors need be considered. 3.3.3.1.4 Since the design of the whole or of any part of a structure may be controlled by any of the load combinations, consider each in design, and adopt the most severe. 3.3.3.1.5 If the probable effect of excessive loads caused by misuse or accident has to be considered in the design, take the γf factor for the overload as 1,05, and consider this only in conjunction with the sustained loads at the ULS. When considering the continued stability of the structure after it has sustained localized damage, consider only the sustained portion of the loads at the ULS. NOTE - In general, the effect of creep, shrinkage and temperature will be of secondary importance for the ULS, and no specific calculations will be necessary.
3.3.3.2 Materials When assessing the strength of a structure or of any part thereof, take the appropriate values of γm as follows:
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SABS 0100-1 Ed. 2.2 a) reinforcement: γm = 1,15 b) concrete in flexure or axial load: γm = 1,50 c) shear strength without shear reinforcement and shear taken by concrete in combination with shear reinforcement: γm = 1,40 d) bond strength: γm = 1,40 e) others (e.g. bearing stresses): γm > 1,50 NOTE - When considering the effects of excessive loads or localized damage, take values of γ m as 1,3 for concrete and 1,0 for steel.
3.3.4 Values for serviceability limit states (loads and materials) 3.3.4.1 Design loads 3.3.4.1.1 Take the design loads for SLS in accordance with clause 4 of SABS 0160 (as amended). 3.3.4.1.2 When assessing the deflection of a structure or of any part thereof, so arrange the imposed load as to cause the largest deflection. 3.3.4.1.3 The design loads given above apply when the immediate deflections of a structure (see 3.2.3.2) are being estimated, but in most cases it is also necessary to estimate the additional time-dependent deflections due to creep, shrinkage and temperature. 3.3.4.1.4 The deflection due to creep depends on the self-weight load and those imposed loads of long duration. Where the full imposed load is unlikely to be permanent, calculate the deflection due to creep on the assumption that only the self-weight load and that part of the imposed load likely to be permanent are effective. This deflection could be upward. Consider the effects of temperature, including temperature gradients within the elements, when these effects exceed those known from experience to be inconsequential. 3.3.4.1.5 When an imposed load is predominantly cyclic in character, give special attention to the assessment of the deflections. 3.3.4.1.6 When assessing crack widths (see 3.2.3.3) or other forms of local damage in a structure subjected to temperature, creep or shrinkage effects exceeding those known from experience to be inconsequential, consider the resulting internal forces and their effect on the structure as a whole. 3.3.4.2 Materials When assessing the deflections of a structure or of any part thereof, take the appropriate values of γm as 1,0 for both concrete and steel. Thus, take the properties of the materials relevant to deflection assessment, i.e. moduli of elasticity, creep, shrinkage, etc., as those associated with the characteristic strength of the materials (see 3.4.2.2 to 3.4.2.4). When assessing the cracking strength of prestressed concrete elements by tensile stress criteria, γm should be taken as 1,3 for concrete in tension due to flexure and 1,0 for steel.
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SABS 0100-1 Ed. 2.2 3.4 Analysis 3.4.1 General The analysis that is carried out to justify a design may be divided into two stages, as follows: a) analysis of the structure; and b) analysis of cross-sections. When the structure or any part thereof is being analysed to determine force distributions within the structure, the properties of materials should be assumed to be those associated with their characteristic strength, irrespective of which limit state is being considered. In the analysis of any cross-section within the structure, the properties of the materials should be assumed to be those associated with their design strength, appropriate to the limit state being considered. Base the methods of analysis used on a representation of the behaviour of the structure that is as accurate as is reasonably practicable. The methods and assumptions given in this clause are generally adequate. In certain cases, advantages may result from the use of more fundamental approaches in assessing the behaviour of the structure under load. (Specific guidance on assumptions and methods that may be used for the serviceability limit states is given in annex A.)
3.4.2 Properties of materials 3.4.2.1 Modulus of elasticity (concrete) 3.4.2.1.1 Unless better information is available for normal density concrete, use the relevant short-term modulus of elasticity given in table 1, appropriate to the serviceability limit states. Table 1 - Values for modulus of elasticity of concrete, E c 1
2
Cube strength of concrete at the appropriate age or stage under consideration
Modulus of elasticity of concrete, Ec
MPa
GPa
20 25 30
25 26 28
40 50 60
31 34 36
For concrete of low density aggregate that has a density in the range 1 400 kg/m 3 to 2 300 kg/m3, Dc2 multiply the values given in table 1 by , where Dc is the density of the low density aggregate 2 300 concrete, in kilograms per cubic metre.
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SABS 0100-1 Ed. 2.2 3.4.2.1.2 Concrete made from certain aggregates (such as certain sand-stones, limestones and granites) could have a modulus of elasticity significantly lower than the values given in table 1. Test such aggregates in order to obtain an appropriate modulus of elasticity for use in design calculations. (Further information on the modulus of elasticity of concrete is given in annex C.) 3.4.2.1.3 For sustained loading conditions, make appropriate allowance for shrinkage and creep. 3.4.2.2 Poisson's ratio (concrete)
For the serviceability limit states, take Poisson's ratio as 0,2. 3.4.2.3 Modulus of elasticity (steel)
For reinforcement, take the modulus of elasticity for all types of loading as E, = 200 GPa. For prestressing tendons, take the short-term modulus of elasticity as -
E, = 205 GPa for high-tensile steel wire,
-
Es = 195 GPa for -/-wire strand,
-
E, = 165 GPa for high-tensile alloy steel bars.
For sustained loading conditions, make appropriate allowance for relaxation. 3.4.2.4 Creep and drying shrinkage
For information on creep and drying shrinkage, consult specialist literature. (But see also annex C.)
3.4.3 Analysis (ultimate limit state) 3.4.3.1 Analysis of structures
The primary objective of structural analysis is to obtain a set of internal forces and moments throughout the structure that are in equilibrium with the design loads for the required loading combination. A redistribution of the calculated forces may be made if the members concerned possess adequate ductility. Generally, it will be satisfactory to determine envelopes of forces and moments by linear elastic analysis of the structure or of any part thereof and to allow for redistribution and possible buckling effects, using the methods described in clauses 4 and 5. When slabs are being considered, the yield line or other appropriate plastic theory may be used. When linear elastic analysis is used, base the relative stiffnesses of the elements throughout on the properties of any one of the following sections: a) the concrete section: the entire concrete cross-section, ignoring the reinforcement; b) the gross section: the entire concrete cross-section, including the reinforcement on the basis of modular ratio; and c) the transformed section: the compression area of the concrete cross-section combined with the reinforcement on the basis of modular ratio. (But see 4.2.4(e).) 3.4.3.2 Analysis of cross-sections
The strength of a cross-section at the ULS, under both short-term and long-term loading, may be taken from the short-term design stress strain curves, as follows:
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SABS 0100-1 Ed. 2.2 a) for normal density concrete, from figure 1 with γm having the relevant value given in 3.3.3.2; b) for reinforcement, from figure 2 with γm having the relevant value given in 3.3.3.2; c) for prestressing reinforcement, from figure 3, with γm having the relevant value given in 3.3.3.2. The strain distribution in concrete and the strains in reinforcement are derived from the assumption that plain sections remain plain. The tensile strength of concrete is ignored. For prestressing tendons, make appropriate allowance for relaxation; for concrete, make appropriate allowance for shrinkage and creep.
3.4.4 Analysis (serviceability limit states) 3.4.4.1 Analysis of structures When elastic analysis is used to determine force distribution throughout the structure, base the relative stiffness on the concrete section, the gross section or the transformed section (see 3.4.3.1). 3.4.4.2 Analysis of cross-sections When assessing the deflections of a structure, calculate the curvature at any section, taking into account the influence of creep, shrinkage and cracking.
3.4.5 Model analysis and testing Deem a design to be satisfactory on the basis of satisfactory results from an appropriate model test coupled with the use of model analysis to predict the behaviour of the actual structure, provided the work has been carried out by engineers with the relevant experience and using suitable equipment.
3.4.6 Experimental development of analytical procedures Deem a design to be satisfactory if the analytical or empirical basis of the design has been justified by development testing of prototype units and structures, relevant to the particular design under consideration.
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SABS 0100-1 Ed. 2.2
NOTES 1 The coefficient 0,67 takes into account the difference between laboratory and site strength of concrete. 2 fcu is in megapascals. 3 For non-linear analysis, specialist literature should be consulted.
Figure 1 — Short-term design stress strain curve for normal density concrete
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SABS 0100-1 Ed. 2.2 | | | | | | | | | | | | | | | | | | | || |
Amdt 1, Apr. 1994 NOTE – fy is in megapascals.
Figure 2 — Short-term design stress strain curve for reinforcement Amdt 1, Apr. 1994
Figure 3 — Short-term design stress strain curve for prestressing reinforcement
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SABS 0100-1 Ed. 2.2
4 Reinforced concrete (design and detailing) 4.1 General This clause gives methods of analysis and design that will, in general, ensure that for reinforced concrete structures, the objectives set out in clause 3 are achieved. Other methods may be used, provided that they can be shown to be satisfactory for the type of structure or element under consideration. In certain cases, the assumptions made in this clause may be inappropriate and the engineer will have to adopt a more suitable method, bearing in mind the nature of the structure in question.
4.1.1 Basis of limit states design This subclause follows the limit states principles set out in clause 3. It is assumed that for reinforced concrete structures, the critical limit state will be the ultimate limit state (see 3.2.2). The design methods therefore take into account the partial safety factors appropriate to the ultimate limit state, and are followed by recommendations to ensure that the serviceability limit states of deflection, cracking or vibration are not reached. The serviceability limit states of deflection and cracking will not normally be reached if the recommendations given for span/effective depth ratios and reinforcement spacings are followed. The engineer may alternatively calculate deflections and crack width to prove compliance with clause 3. (Suitable methods are described in annex A.)
4.1.2 Stability Apart from the considerations given in 3.2.2, cognizance should also be taken of those given below: 4.1.2.1 Ultimate horizontal load All structures should be capable of resisting an ultimate horizontal load applied at each floor and roof level simultaneously, of at least 1,5 % of the nominal self-weight of the structure between mid-height of the storey below and either mid-height of the storey above or the roof surface. This force could be shared by the parts of the structure, depending on their stiffness and strength. 4.1.2.2 Safeguarding against vehicular impact In order to obviate the possibility of vehicles running into and damaging or destroying vital load-bearing elements in the ground floor of a structure, the provision of elements such as bollards, walls and retaining earthbanks should be considered. 4.1.2.3 Provision of ties In structures where all load-bearing elements are of concrete, horizontal and vertical ties should be provided in accordance with 4.11.9.
4.1.3 Durability and fire resistance The durability and the fire resistance of reinforced concrete depend on the amount of concrete cover to reinforcement. Guidance on the minimum cover to reinforcement that is necessary to ensure durability is given in 4.11.2. Fire test results or other evidence may be used to ascertain the fire resistance of an element or, alternatively, reference could be made to clause 7.
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SABS 0100-1 Ed. 2.2 4.1.4 Loads In this clause, the design load for the ultimate limit state is referred to as the ultimate load or the maximum design load, to avoid confusion with the service load, which is the design load for the serviceability limit states. In design, use the values of the ultimate loads given in 3.3.3.1, and the values of the service loads given in 3.3.4.1.
4.1.5 Strength of materials In this clause, the design strengths of materials for the ultimate limit state are expressed (in all the tables and equations) in terms of the characteristic strength of the material. Unless specifically stated otherwise, all equations and tables include allowances for γm, the partial safety factor for material strength. 4.1.5.1 Characteristic strength of concrete The values of the 28 d characteristic strength of concrete, fcu, and the required strength of concrete at ages exceeding 28 d, for various grades of concrete, are given in table 2. Table 2 - Strength of concrete 1
2
3
4
5
Required strength at other ages
Grade
Characteristic strength, fcu
MPa
MPa
months
Age
3
6
12
20 25 30
20,0 25,0 30,0
23 29 34
24 30 35
25 31 36
35 40 45 50
35,0 40,0 45,0 50,0
39 44 49 54
40 46 51 56
42 48 53 58
Design consideration should be based on the characteristic strength fcu, or, if relevant, on the appropriate strength given in table 2 for the age at loading. For reinforced concrete, the lowest grade that should be used is 20 for concrete made with normal-weight aggregates and 15 for concrete made with lightweight aggregates. 4.1.5.2 Characteristic strength of reinforcement Base the design on the appropriate characteristic strength of reinforcement given in table 3. (If necessary, a lower design stress may be used to help control deflection or cracking, and possibly a different grade of reinforcement may be used.)
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SABS 0100-1 Ed. 2.2 Table 3 -Characteristic strength of reinforcement, f, 1
2
3
Designation of reinforcement
Nominal sizes
Characteristic strength f,
mm
MPa
Hot-rolled mild steel (SABS 920)
All sizes
250
Hot-rolled high-yield steel (SABS 920)
All sizes
450
Cold-work high-yield steel (SABS 920)
All sizes
450
Up to and including 12
485
Hard-drawn steel wire
4.1.6 Other considerations For recommendations concerning vibration or other limit states, refer to clause 3. For comment on the deterioration of concrete as a result of chemical aggresion, refer to SABS 0100-2.
4.2 Analysis of structures and structural frames 4.2.1 Analysis of complete structures and complete structural frames Analysis may be in accordance with 3.4.3 or, when appropriate, by the methods given in 4.2.2. NOTE -In the case of frame structures, ensure that if failure were to occur in critical conditions, it would occur in the beams and not in the columns.
4.2.2 Analysis of structural frames supporting vertical loads only 4.2.2.1 Simplification into subframes When a frame supporting vertical loads only is assumed, the moments, loads and shear forces to be used in the design of individual columns and beams may be derived from an elastic analysis of a series of subframes (but see 4.2.4 concerning redistribution of moments). Each subframe may be taken to consist of the beams at one level together with the columns above and below. The ends of the columns remote from the beams may generally be assumed to be fixed, unless the assumption of a pinned end is clearly more reasonable (for example where a foundation detail is considered unable to develop moment restraint). It will normally be sufficient to consider the following critical arrangements of vertical load: all spans loaded with total ultimate load (1,2Gn+ 1,6Q,); all spans loaded with ultimate self-weight load (1,2Gn) and alternate spans loaded with ultimate imposed load (1,6Q,).
4.2.2.2 Alternative simplification of subframes (individual beams with associated columns) As an alternative to 4.2.2.1, the moments and forces in each individual beam may be found by considering a simplified subframe consisting only of that beam, the columns attached to the ends of the beam and the beams on either side, if any. The column ends and the beam ends remote from the
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SABS 0100-1 Ed. 2.2 beam under consideration may generally be assumed to be fixed, unless the assumption of pinned ends is clearly more reasonable. The stiffness of the beams on either side of the beam under consideration should be taken as half their actual stiffness values if they are taken to be fixed at their outer ends. The critical loading arrangements should be taken as follows: – all spans loaded with total ultimate load (1,2G n + 1,6Qn); | |
– all spans loaded with ultimate self-weight load (1,2Gn) and alternate spans loaded with ultimate Amdt 1, Apr. 1994 imposed load (1,6Qn). The moments in an individual column may also be found from this simplified subframe, provided that the subframe has at its central beam the longer of the two spans framing into the column under consideration. 4.2.2.3 "Continuous beam" simplification As a more conservative alternative to the preceding subframe arrangements, the moments and shear forces in the beams at one level may also be obtained by regarding the beams as a continuous beam over supports providing no restraint to rotation. The critical loading arrangements should be in accordance with 4.2.2.1. 4.2.2.4 Asymmetrically loaded columns where a beam has been analysed in accordance with 4.2.2.3 In these columns, the ultimate moments may be calculated by simple moment distribution procedures, on the assumption that the columns and beam ends remote from the junction under consideration are fixed and that the beams possess half their actual stiffness. The arrangement of the design ultimate imposed load should be such as to cause the maximum moment in the column.
4.2.3 Analysis of structural frames supporting vertical and lateral loads 4.2.3.1 When a frame provides lateral stability to the structure as a whole, it will be necessary to consider the effect of lateral loads. In addition, if the columns are slender (see 4.7.1.4), it may be necessary to consider additional moments (e.g. from eccentricity) that may be imposed on beams at beam column junctions. 4.2.3.2 In most cases, the design of individual beams and columns may be based either on the moments, loads and shears obtained by considering vertical loads only (as in 4.2.2) or on those obtained by considering both vertical and lateral loads. If the moments, loads and shears obtained by considering both types of loads are greater than those obtained by considering vertical loads only, then the design should be based on the sum of those obtained from 4.2.3.2.1 and 4.2.3.2.2. 4.2.3.2.1 An elastic analysis of a series of subframes, each consisting of the beams at one level together with the columns above and below. The ends of the columns remote from the beams may generally be assumed to be fixed, unless the assumption of pinned ends is clearly more reasonable. NOTE - Lateral loads should be ignored and all beams should be considered to be loaded as in 4.2.2.
4.2.3.2.2 An analysis of the complete frame, assuming points of contraflexure at the centres of all beams and columns, ignoring self-weight and imposed loads and considering only the design wind load on the structure. If more realistic, instead of assuming points of contraflexure at the centres of ground floor columns, the feet should be considered pinned.
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SABS 0100-1 Ed. 2.2 4.2.4 Redistribution of moments Redistribution of the moments obtained by elastic analysis or by the simplified methods given in 4.2.2 and 4.2.3 may be carried out, provided the following conditions are satisfied: a)
condition 1: equilibrium between internal and external forces is maintained under all appropriate combinations of ultimate load.
b)
condition 2: where the design ultimate resistance moment of the cross-section subjected to the largest moment within each region of hogging or sagging is reduced, the neutral axis depth x should not exceed (βb-0,4)d
where d is the effective depth; and βb =
(moment at section after redistribution) 5
β 0,14 0,20 0,23 0,26 0,29 0,33
A formula which gives values of × within 4 % is
× ' 0,33 & 0,21
hmin hmax
4
1 &
hmin 4
12hmax
The St. Venant torsional stiffness of a non-rectangular section may be obtained by dividing the section into a series of rectangles and summing the torsional stiffness of these rectangles. The division of the section should be so arranged as to maximize the calculated stiffness. (This will generally be achieved if the widest rectangle is made as long as possible.) 4.3.5.3 Torsional shear stress vt 4.3.5.3.1 Rectangular sections The torsional shear stress vt at any section should be calculated assuming a plastic stress distribution and may be calculated from the following equation:
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SABS 0100-1 Ed. 2.2 2T
vt = 2
hmin
hmax
hmin 3
where T
is the torsional moment due to design loads for the ultimate limit state;
hmin
is the smaller dimension of rectangular section; and
hmax is the larger dimension of rectangular section. 4.3.5.3.2 T-, L- or I-sections T-, L- or I-sections may be treated by dividing them into their component rectangles; these are chosen in such a way as to maximize h3min x hmax, which will generally be achieved if the widest rectangle is made as long as possible. Then 4.3.5.3.1 should be followed, bearing in mind that each of these component rectangles is subjected to a torsional moment as follows: 3
T T
hmin hmax 3 (hmin
hmax)
where T is the partial torsional moment. 4.3.5.3.3 Box sections Box sections in which wall thicknesses exceed one-quarter of the overall thickness of the beam in the direction of measurement may be treated as solid rectangular sections. In the case of other sections, consult specialist literature. 4.3.5.3.4 Reinforcement for torsion Where the torsion shear stress vt exceeds the value vt,min in table 8, reinforcement should be provided. In no case may the sum of the shear stresses resulting from shear force and torsion (v + vt) exceed the value vtu in table 8 nor, in the case of small sections (y1 < 550 mm), shall the torsion shear stress vt exceed vtu y1/550, where y1 is the larger centre-to-centre dimension of a link.
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SABS 0100-1 Ed. 2.2 Table 8 Minimum and ultimate torsional shear stress
|
Amdt 1, Apr. 1994 Values in megapascals 1
2
3
Concrete grade
Minimum torsional shear stress, vt,min
Ultimate torsional shear stress, vtu
0,27 0,30 0,33 0,36
3,18 3,56 4,00 4,50 < vtu < 4,75
*)
20 25 30 > 40
*)Grade not recommended. NOTES 1 Allowance has been made in these figures for a γm of 1,40. 2 Values of vtu are derived from the equation
vtu 0,71 f cu but not exceeding 4,75 MPa.
Recommendations for reinforcement for combinations of shear and torsion are given in table 9.
Table 9 Reinforcement for shear and torsion 1
2
3
vt < vt,min
vt > vt,min
v < vc + 0,4
Minimum shear reinforcement; no torsion reinforcement
Designed torsion reinforcement but not less than the minimum shear reinforcement
v > vc + 0,4
Designed shear reinforcement; no torsion reinforcement
Designed shear and torsion reinforcement
4.3.5.3.5 Area of torsional reinforcement Torsional reinforcement should consist of rectangular closed links together with longitudinal reinforcement. This reinforcement is additional to any requirements for shear and bending and should be such that Asv sv
34
T 0,8 x1 y1 (0,87 f yv)
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SABS 0100-1 Ed. 2.2 As
Asv f yv (x1 y1) sv f y
where Asv is the area of two legs of closed links at a section (in a section reinforced with multiple links, the area of the legs lying closest to the outside of the section should be used); As is the area of longitudinal reinforcement; fyv
is the characteristic strength of links (but not exceeding 450 MPa);
fy
is the characteristic strength of longitudinal reinforcement (but not exceeding 450 MPa);
sv
is the spacing of links;
x1
is the smaller centre-to-centre dimension of rectangular link; and
y1
is the larger centre-to-centre dimension of rectangular link.
4.3.5.3.6 Spacing and type of links The spacing of the links sv should not exceed the least of x1, y1/2 and 200 mm. The links should be of a closed type similar to code 74 links of SABS 82. 4.3.5.3.7 Arrangement of longitudinal torsional reinforcement Longitudinal torsional reinforcement should be distributed evenly round the inside perimeter of the links. The clear distance between these bars should not exceed 300 mm, and at least four bars, one in each corner of the links, should be used. Additional longitudinal reinforcement required at the level of the tension or compression reinforcement may be provided by using larger bars than those required for bending only. The torsional reinforcement should extend for a distance at least equal to the largest dimension of the section beyond where it theoretically ceases to be required. 4.3.5.3.8 Arrangement of links in T-, L- or I-sections In the component rectangles, the reinforcement cages should be so detailed that they interlock and tie the component rectangles of the section together. Where the torsional shear stress in a minor component rectangle is less than vt,min, no torsional reinforcement need be provided in that rectangle.
4.3.6 Deflection of beams 4.3.6.1 General Deflection may be calculated (see annex A) and compared with the serviceability requirements given in 3.2.3.2, but in all normal cases, the deflection of a beam will not be excessive if the ratio of its span to its effective depth does not exceed the appropriate ratio obtained from 4.3.6.2 or 4.3.6.3. When appropriate, use the modification factors given in tables 11 and 12 to modify the ratios given in table 10. 4.3.6.2 Span/effective depth ratio for rectangular beams 4.3.6.2.1 The basic span/effective depth ratios for rectangular beams are given in table 10. These are based on limiting the deflection to span/250 and this should normally prevent damage to finishes and
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SABS 0100-1 Ed. 2.2 partitions for beams of span up to 10 m (see 3.2.3.2). For cantilevers, add or subtract, as appropriate, the support rotation times the cantilever span. Table 10 - Basic span/effective depth ratios for rectangular beams 1
2
Support conditions
Ratio
Truly simply supported beams Simply supported beams with nominally restrained ends Beams with one end continuous Beams with both ends continuous Cantilevers
16 20 24 28 7
4.3.6.2.2 Table 10 may be used for spans exceeding 10 m but only when it is not necessary to limit the increase in deflection after the construction of partitions and finishes. Otherwise, in order to prevent damage to finishes and partitions, the values given in table 10 should be multiplied by 10/span, except for cantilevers, where the design should be justified by calculation. 4.3.6.3 Modification of span/effective depth ratios for reinforcement 4.3.6.3.1 Tension reinforcement | |
Since deflection is influenced by the amount of tension reinforcement and its stresses, it is necessary to modify the span/effective depth ratios according to the ultimate design moment and the service stress at the centre of the span (or at the support in the case of a cantilever). Therefore, values of span/effective depth ratio obtained from table 10 should be multiplied by the appropriate factor Amdt 1, Apr. 1994 obtained from table 11.
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SABS 0100-1 Ed. 2.2 Table 11 - Modification factors for tension reinforcement 1
2
3
4
5
6
7
8
9
10
11
12
13
Modification factors
Steel service stress
M/bd 2 0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
5,0
5,5
6,0
300 290 280
1,60 1,66 1,72
1,33 1,37 1,41
1,16 1,20 1,23
1,06 1,09 1,12
0,98 1,01 1,03
0,93 0,95 0,97
0,89 0,90 0,92
0,85 0,87 0,89
0,82 0,84 0,85
0,80 0,81 0,83
0,78 0,79 0,81
0,76 0,78 0,79
270 260 250
1,78 1,84 1,90
1,46 1,50 1,55
1,27 1,30 1,34
1,14 1,17 1,20
1,06 1,08 1,11
0,99 1,01 1,04
0,94 0,96 0,98
0,90 0,92 0,94
0,87 0,88 0,90
0,84 0,86 0,87
0,82 0,83 0,85
0,80 0,81 0,82
240 230 220
1,96 2,00 2,00
1,59 1,63 1,68
1,37 1,41 1,44
1,23 1,26 1,29
1,13 1,16 1,18
1,06 1,08 1,10
1,00 1,02 1,04
0,95 0,97 0,99
0,92 0,93 0,95
0,88 0,90 0,91
0,86 0,87 0,88
0,84 0,85 0,86
210 200 190
2,00 2,00 2,00
1,72 1,76 1,81
1,48 1,51 1,55
1,32 1,35 1,37
1,20 1,23 1,25
1,12 1,14 1,16
1,06 1,07 1,09
1,00 1,02 1,04
0,96 0,98 0,99
0,93 0,94 0,96
0,90 0,91 0,92
0,87 0,88 0,90
180 170 160
2,00 2,00 2,00
1,85 1,90 1,94
1,58 1,62 1,65
1,40 1,43 1,46
1,28 1,30 1,33
1,18 1,21 1,23
1,11 1,13 1,15
1,06 1,07 1,09
1,01 1,02 1,04
0,97 0,98 1,00
0,94 0,95 0,96
0,91 0,92 0,93
150 140 130 120
2,00 2,00 2,00 2,00
1,98 2,00 2,00 2,00
1,69 1,72 1,75 1,79
1,49 1,52 1,55 1,58
1,35 1,38 1,40 1,43
1,25 1,27 1,29 1,31
1,17 1,19 1,21 1,23
1,11 1,12 1,14 1,16
1,05 1,07 1,09 1,10
1,01 1,03 1,04 1,05
0,98 0,99 1,00 1,01
0,94 0,96 0,97 0,98
NOTES 1 The values in the table are based on the formula: Modification factor = 0,55 +
(477 f s)
< 2,0
M 120 0,9 bd 2 where M b d fs
is the design ultimate moment at the centre of the span or, for cantilevers, at the support; is the width of section; is the effective depth of section; and is the design estimate service stress in tension reinforcement.
2 For flanged beams, see 4.3.6.5. 3 Span considered is smaller span for 2-way slabs, larger for flat slabs. 4 For flat plates (no drops), multiply factor by 0,9.
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SABS 0100-1 Ed. 2.2 The design service stress in the tension reinforcement in a beam may be estimated from the following equation:
fs
|
= 0,87 f y x
Ø1 Ø3
% %
Ø2 Ø4
x
As,req As,prov
x
1 ×b
Amdt 1, Apr. 1994
where fs
is the estimated service stress in tension reinforcement;
fy
is the characteristic strength of reinforcement;
Ø1
is the self-weight load factor for serviceability limit states;
Ø2
is the imposed load factor for serviceability limit states;
Ø3
is the self-weight load factor for ultimate limit state;
Ø4
is the imposed load factor for ultimate limit state;
As,req
is the area of tension reinforcement required at mid-span to resist moment due to ultimate loads (at the support in the case of a cantilever);
As,prov
is the area of tension reinforcement provided at mid-span (at the support in the case of a cantilever); and
βb
is the ratio of resistance moment at mid-span obtained from redistributed maximum moments diagram to that obtained from maximum moments diagram before redistribution.
If the percentage of redistribution is not known but the design ultimate moment of mid-span is clearly the same or exceeds the elastic ultimate moment, the stress fs given in table 11 may be calculated from the above equation where βb = 1,0. 4.3.6.3.2 Compression reinforcement Because compression reinforcement also influences deflection, the value of the span/effective depth ratio modified in accordance with table 11 may be multiplied by a further factor obtained from table 12.
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SABS 0100-1 Ed. 2.2 Table 12 - Modification factors for compression reinforcement 1
2
100As
Factor*)
bd 0,15 0,25 0,35
1,05 1,08 1,10
0,50 0,75 1,00
1,14 1,20 1,25
1,25 1,50 1,75
1,29 1,33 1,37
2,00 2,50 > 3,00
1,40 1,45 1,50
*)Obtain intermediate values by interpolation. The area of compression reinforcement at midspan As) used in table 12 may comprise all bars in the compression zone, including those not effectively tied with links.
4.3.6.4 Deflection due to creep and shrinkage Permissible span/effective depth ratios obtained from tables 9 to 11 take account of normal creep and shrinkage deflection. If it is expected that creep or shrinkage of the concrete might be particularly high (concrete of very poor quality and workmanship, high long-term loadings), i.e. the free shrinkage stress exceeds 0,000 75 or the creep coefficient exceeds 4, the permissible span/effective depth ratio should be reduced. A reduction of more than 15 % is unlikely to be required. 4.3.6.5 Span/effective depth ratio for flanged beams For a flanged beam, the span/effective depth ratio may be determined as in 4.3.6.2 but, when the web width is less than 0,3 times the effective flange width, multiply the final ratio obtained by 0,8. For values of web width to effective flange width that exceed 0,3, this factor may be increased linearly from 0,8 to 1,0 as the ratio of web width to effective flange width increases to unity. In the case of inverted flanged beams with the flange in tension, the tension reinforcement within the width of the web must be taken into consideration. The compression reinforcement (as in table 12) should be that within the effective width of the flange.
4.3.7 Crack control in beams In general, compliance with the reinforcement spacing rules given in 4.11.8 will be an acceptable method of controlling flexural cracking in beams, but in certain cases, particularly where groups of bars are used, advantage may be gained from calculating crack widths (see annex A) and comparing them with the recommended values given in clause 3.
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SABS 0100-1 Ed. 2.2 4.4 Solid slabs 4.4.1 Design of solid slabs In general, the recommendations given in 4.3 for beams will apply also to solid slabs, but take 4.4.2 to 4.4.7 into account.
4.4.2 Moments and forces in solid slabs 4.4.2.1 General In solid slabs, the moments and shear forces resulting from both distributed and concentrated loads may be found as for beams. They may also be determined by elastic analyses such as those of Pigeaud and Westergaard. Alternatively, Johansen's yield-line method or Hillerborg's strip method may be used, provided that the ratios between support and span moments are similar to those obtained by the use of the elastic theory. Values in the range 1,0 to 1,5 are recommended. 4.4.2.2 Resistance moments of solid slabs The ultimate moment of resistance of a cross-section in a solid slab may be determined by using the methods given in 4.3.3 for beams. 4.4.2.3 Simplification of load arrangements A continuous slab will be able to withstand the most unfavourable arrangements of design loads if it is designed to resist the moments and forces arising from the single-load case of maximum design load on all spans. The following conditions are to be met: a)
in a one-way spanning slab, the area of each bay exceeds 30 m2.
NOTE - In this context, a bay is a strip across the full width of a structure and supported on two sides (see figure 7).
Figure 7 — Definition of panels and bays
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SABS 0100-1 Ed. 2.2 b)
the ratio of the characteristic imposed load to the characteristic self-weight load does not exceed 1,25.
c)
the characteristic imposed load does not exceed 5 kN/m2, excluding partitions.
When analysis is carried out for the single-load case of maximum design load on all spans, the resulting support moments, except those at the support of cantilevers, should be reduced by 20 %, with a resultant increase in the span moments (see 4.2.4). When a span is adjacent to a cantilever of length exceeding one-third of the span of the slab, the other possibility of loading arrangement should be considered, i.e. the case of slab unloaded and the cantilever loaded. d)
steel curtailment complies with the simplified rules for curtailment given in 4.11.7.3.
4.4.2.4 Distribution of concentrated loads on slabs If a slab is simply supported on two opposite edges and carries one or more concentrated loads in a line in the direction of the span, the maximum bending moments may be assumed to be resisted by an effective width of slab (measured parallel to the supports), given below. 4.4.2.4.1 For solid slabs, the effective width may be taken as the sum of the load width plus 2,4x(1- x/l) where x is the distance from the nearer support to the section under consideration and l is the span. For cantilever slabs the equivalent value is 2,4x. 4.4.2.4.2 For slabs other than solid slabs, the effective width will depend on the ratio of the transverse and longitudinal flexural rigidities of the slab. The minimum value to be taken, however, is the load width plus 4 x/l (1- x/l) metres where x and l are as defined in 4.4.2.4.1, such that, for a section at mid-span, the effective width is equal to 1 m plus the load width. 4.4.2.4.3 Where the concentrated load is near an unsupported edge of a slab, the effective width should not exceed the value given in 4.4.2.4.1 or 4.4.2.4.2, as appropriate, nor half that value plus the distance of the centre of the load from the unsupported edge (see figure 8).
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SABS 0100-1 Ed. 2.2
Figure 8 — Effective width of solid slab carrying a concentrated load near an unsupported edge
4.4.3 One-way spanning slabs of approximately equal span Where the length of the longer side of a slab exceeds three times the length of the shorter side, so design the slab as to span one way only. When the conditions of 4.4.2.3 are met, the moments and shears in continuous one-way spanning slabs may be calculated using the coefficients given in table 13. Table 13 - Ultimate bending moments and shear forces in one-way spanning slabs 1
2
3
Position
Moment
Shear
At outer support Near middle of end span At first interior support
0 0,086 Fl -0,086 Fl
0,4F 0,6F
At middle of interior spans At interior supports
0,063 Fl -0,063 Fl
0,5F
NOTE - F is the total ultimate load (1,2Gn + 1,6Qn).
Allowance has been made in these coefficients for 20 % redistribution. No further redistribution should be carried out. (See also 4.2.4 (d).)
42
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SABS 0100-1 Ed. 2.2 The curtailment of reinforcement designed in accordance with table 13 may be carried out in accordance with the rules given in 4.11.7.3.
4.4.4 Solid slabs spanning in two directions at right angles (uniformly distributed loads) In addition to other methods, the methods given in 4.4.4.1 to 4.4.4.3 may be used for the design of slabs spanning in two directions at right angles and supporting uniformly distributed loads. 4.4.4.1 Simply supported slabs When simply supported rectangular slabs do not have adequate provision to resist torsion at the corners and to prevent the corners from lifting, the maximum moments per unit width are given by the following equations: Msx= sxnl
2
Msy= synl
2
x x
where Msx, Msy
are the maximum bending moments at mid-span on strips of unit width spanning lx and ly, respectively;
n
is the total ultimate load per unit area (1,2 gn + 1,6 qn);
lx
is the length of shorter side;
ly
is the length of larger side; and
αsx, αsy
are the bending moment coefficients given in table 14.
Extend to the supports at least 50 % of the tension reinforcement provided at mid-span. Extend the remaining part of the reinforcement to within 0,1l x or 0,1l y of the support, as appropriate.
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SABS 0100-1 Ed. 2.2 Table 14 - Bending moment coefficients for slabs spanning in two directions at right angles, simply supported on four sides 1
2
3
ly lx
αsx
αsy
1,0 1,1 1,2
0,045 0,061 0,071
0,045 0,038 0,031
1,3 1,4 1,5
0,080 0,087 0,092
0,027 0,023 0,020
1,6 1,7 1,8
0,097 0,100 0,102
0,017 0,015 0,016
1,9 2,0 2,5 3,0
0,103 0,104 0,108 0,111
0,016 0,016 0,016 0,017
4.4.4.2 Restrained slabs Both in continuous and in discontinuous slabs where the corners are prevented from lifting and provision for torsion is made, the maximum moments per unit width are given by the following equations: Msx = βsxnl2x
(3)
Msy = βsynl2x
(4)
where
44
Msx, Msy
are the maximum bending moments at mid-span on strips of unit width spanning lx and ly, respectively;
n
is the total ultimate load per unit area (1,2 gn + 1,6 qn);
lx
is the length of shorter side;
ly
is the length of larger side; and
βsx, βsy
are the bending moment coefficients given in table 15.
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 Table 15 - Bending moment coefficients for rectangular panels supported on four sides with provision for torsional reinforcement at the corners 1
2
3
4
5
6
7
8
9
Short-span coefficients βsx Case
1
2
3
4
5
6
7
8
9
Type of panel and moments considered
Values of ly/lx
10
Long-span coefficients, βsy for all values of ly/lx
1,0
1,1
1,2
1,3
1,4
1,5
1,75
2,0
Interior panels Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,031 0,024
0,037 0,028
0,042 0,032
0,046 0,036
0,050 0,039
0,053 0,041
0,059 0,045
0,063 0,049
0,032 0,024
One short edge discontinuous Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,039 0,029
0,044 0,033
0,048 0,036
0,052 0,039
0,055 0,041
0,058 0,043
0,063 0,047
0,067 0,050
0,037 0,028
One long edge discontinuous Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,039 0,030
0,049 0,036
0,056 0,042
0,062 0,047
0,068 0,051
0,073 0,055
0,082 0,062
0,089 0,067
0,037 0,028
Two adjacent edges discontinuous Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,047 0,036
0,056 0,042
0,063 0,047
0,069 0,051
0,074 0,055
0,078 0,059
0,087 0,065
0,092 0,070
0,045 0,034
Two short edges discontinuous Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,046 0,034
0,050 0,038
0,054 0,040
0,057 0,043
0,060 0,045
0,062 0,045
0,067 0,047
0,070 0,053
0,034
Two long edges discontinuous Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,034
0,046
0,056
0,065
0,072
0,078
0,091
0,100
0,045 0,034
Three edges discontinuous (one long edge continuous) Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,057 0,043
0,065 0,048
0,071 0,053
0,076 0,057
0,080 0,060
0,084 0,063
0,092 0,069
0,098 0,074
0,044
Three edges discontinuous (one short edge continuous) Negative moment at continuous edge . . . . . . . . . . . . . . . . . . . . . . Positive moment at mid-span . . .
0,042
0,054
0,063
0,071
0,078
0,084
0,096
0,105
0,058 0,044
Four edges discontinuous Positive moment at mid-span . . .
0,055
0,065
0,074
0,081
0,087
0,092
0,103
0,111
0,056
Where these equations are used, the conditions given below apply. 4.4.4.2.1 In the case of continuous slabs The nominal self-weight and imposed loads on adjacent slabs should be approximately the same as those on the slab under consideration, and the spans of all adjacent slabs should be approximately the same in each of the two directions of the lines of the supports. (See also 4.4.4.2.2.) 4.4.4.2.2 In the case of continuous and discontinuous slabs Regard slabs as divided in each direction into middle strips and edge strips as shown in figure 9, the middle strip being three-quarters of the width and each edge strip one-eighth of the width; The maximum moments calculated as in 4.4.4.2 apply to the middle strips only and no redistribution is permitted.
45
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SABS 0100-1 Ed. 2.2
Figure 9 — Division of slab into middle and edge strips a) tension reinforcement at mid-span: extend at least 50 % of the tension reinforcement provided at mid-span in the middle strip in the lower part of the slab to within 0,15l of the continuous edge axis, and to within 50 mm of the discontinuous edge axis; extend the remaining part of the reinforcement to within 0,25l of a continuous edge axis, and to within 0,15l of the discontinuous edge axis; b) tension reinforcement over the continuous edges: extend at least 50 % of the tension reinforcement provided in the upper part of a middle strip to a distance 0,3l from the face of the support; extend the remaining part of the reinforcement to a distance of 0,15l from the face of the support; c) tension reinforcement over the discontinuous edge: at a discontinuous edge, negative moments may arise, depending on the degree of fixity of the edge of the slab; in general, tension reinforcement equal to 50 % of that provided at mid-span extending 0,1l into the span (from the face of the support) will be sufficient; d) tension reinforcement in an edge strip, parallel to the edge: the reinforcement need not exceed the minimum given in 4.11.4 and the minimum given in the rules for torsional reinforcement given in (e), (f) and (g) below; e) torsional reinforcement at any corner where the slab is simply supported on both edges meeting at that corner: the reinforcement should comprise top and bottom reinforcement, each with layers of bars placed parallel to the sides of the slab and extending from the external faces of the edges a minimum distance of one-fifth of the shorter span; the area of reinforcement in each of these four layers should be three-quarters of the area required for the maximum mid-span moment in the slab; f) torsional reinforcement at any corner contained by edges over only one of which the slab is continuous: reinforcement equal to half of that described in (e) above should be provided; g) torsional reinforcement need not be provided at any corner contained by edges over both of which the slab is continuous: where ly /lx exceeds 3, so design slabs as to span one way only.
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SABS 0100-1 Ed. 2.2 4.4.4.2.3 In the case of a restrained slab with unequal conditions at adjacent panels If the support moments for adjacent panels (calculated using table 15) differ significantly, they may be adjusted as follows: a) calculate the sum of the moments at mid-span and supports (ignoring signs); b) treat the values from table 15 as fixed end moments; c) distribute these fixed end moments across the supports according to the relative stiffness of adjacent spans, giving new support moments; d) adjust the mid-span moment; this should be such that when it is added to the support moments as in (c) above (ignoring signs), the total should equal that obtained in (a) above; if, for a given panel, the resulting support moments now significantly exceed the values given by equations (3) and (4), the tension steel over the supports will need to be extended beyond the provisions of 4.11.7.3. The procedure is as follows: 1) the span moment is taken as parabolic between supports; its maximum value is as found in (d) above; 2) the points of contraflexure of the new support moments (as in (c) above) and the span moment (as in (1) above) are determined; 3) at each end, half the support tension steel is extended to at least an effective depth or 12 bar diameters beyond the nearest point of contraflexure; and 4) at each end, the full area of the support tension steel is extended to half the distance obtained in (3) above. 4.4.4.3 Loads on supporting beams The design loads on beams supporting solid slabs spanning in two directions at right angles and supporting uniformly distributed loads may be assumed to be in accordance with figure 10. If the edges of two slabs having the same support meet at a corner, the dividing angle is 45°. If a fully restrained edge meets a freely supported edge, the dividing angle on the restrained side is 60°. With partial restraint, the angles may be assumed to lie between 45° and 60° (see figure 10(b)).
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SABS 0100-1 Ed. 2.2
Figure 10 — Apportionment of load for determining the bearing reactions
4.4.5 Shear resistance of solid slabs 4.4.5.1 Shear stresses in solid slabs The design shear stress v at any cross-section in a solid slab should be compared with the allowable shear stress vc and in no case should it exceed the lesser of
0,75 f cu
or 4,75 MPa, whatever
reinforcement is provided. Calculate v from: v '
V bd
(5)
where v is the design shear stress; V is the shear force due to design maximum loads; b is the width of slab under consideration (usually 1 000 mm); and d is the effective depth; and the allowable stress vc is the maximum design shear stress in concrete without shear reinforcement (obtainable from 4.3.4.1). When the design shear stress v is less than the allowable shear stress vc, no shear reinforcement is needed. When v exceeds vc, shear reinforcement should be provided in accordance with the appropriate rules for beams (see 4.3.4). When links are used in slabs less than 200 mm thick, the partial loss of efficiency of the links should be taken into consideration unless structural steel shear heads are provided that have been designed in accordance with specialist literature. It may be assumed that every 10 mm reduction in the slab thickness reduces the links' efficiency by 10 %.
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SABS 0100-1 Ed. 2.2 The enhancement in design shear strength close to supports (as described in 4.3.4.2) may also be applied to solid slabs. 4.4.5.2 Shear stresses in solid slabs under concentrated load 4.4.5.2.1 The following terms specific to perimeters are used in this subclause: a) perimeter: a boundary of the smallest rectangle (or square) that can be drawn around a loaded area and that nowhere comes closer to the edges of the loaded area than some specified distance lp (a multiple of 0,75d) (see figure 11). NOTE - See 4.4.5.2.8 for loading close to a free edge.
b) failure zone: an area of slab bounded by perimeters 1,5d apart (see figure 12); c) effective length of a perimeter: the length of the perimeter reduced, where appropriate, for the effects of openings or external edges; d) effective depth d: the average effective depth for all effective reinforcement passing through a perimeter; and e) effective steel area: the total area of all tension reinforcement that passes through a zone and that extends at least one effective depth (see above) or 12 times the bar size beyond the zone on either side. NOTE - The reinforcement percentage used to calculate the design ultimate shear stress vc is given by: 100 x effective steel area ud where u is the outer perimeter of zone concerned; and d is the effective depth (as defined above).
49
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SABS 0100-1 Ed. 2.2
Figure 11 — Definition of a shear perimeter for typical cases 4.4.5.2.2 The maximum design shear stress vmax resulting from the concentrated load and calculated as below should not exceed the lesser of vmax
0,75 f cu or 4,75 MPa.
V uo d
(6)
where | | | | |
V
is the design maximum value of concentrated load;
uo
is the effective length of perimeter that touches a loaded area; and
d
is the effective depth of slab.
|
The maximum shear capacity may also be limited by the provisions of 4.4.5.2.6.
| | |
4.4.5.2.3 The shear capacity of punching shear zones is checked first on a perimeter 1,5 d from the face of the loaded area. If the calculated shear stress does not exceed vc, then no further checks are Amdt 1, Apr. 1994 needed.
50
Amdt 1, Apr. 1994
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 If shear reinforcement is required, then it should be provided on at least two perimeters within the zone indicated in figure 12. The first perimeter of reinforcement should be located at approximately 0,5d from the face of the loaded area and should contain not less than 40 % of the calculated area of reinforcement. The spacing of perimeters of reinforcement should not exceed 0,75d and the spacing of the shear reinforcement around any perimeter should not exceed 1,5d. The shear reinforcement should be anchored round at least one layer of tension reinforcement. The shear stress should then be checked on successive perimeters at 0,75d intervals until a perimeter is reached which does not require shear reinforcement. In the provision of reinforcement for the shear calculated on the second and subsequent perimeters, the reinforcement provided for the shear on previous perimeters and that lies within the zone shown in figure 12 should be taken into account. 4.4.5.2.4 The nominal design shear stress v, appropriate to a particular perimeter, is calculated from: V ud
v '
(7)
|
Amdt 1, Apr. 1994
where V, d are as in equation (5); and u
is the effective length of the outer perimeter of the zone.
4.4.5.2.5 No shear reinforcement is required when the stress v is less than vc as calculated in 4.3.4.1. The value of 100 As/bvd to be used in 4.3.4.1 may be taken as the average for the two directions.
| |
Amdt 1, Apr. 1994
In the case of zone 1, As in each direction should include all the tension reinforcement within a strip of width bv equal to the width of the loaded area plus three times the effective depth of slab on either Amdt 1, Apr. 1994 side of the loaded area.
|
The enhancement of vc permitted in 4.3.4.2 should not be applied to the shear strength of perimeters at a distance of 1,5d or more from the face of the loaded area. Where it is desired to check perimeters closer to the loaded area than 1,5d, vc may be increased by a factor 1,5 d/av (up to 4 MPa), where av is the distance from the edge of the loaded area to the perimeter considered. 4.4.5.2.6 The use of shear reinforcement other than links is not covered specifically by this code and Amdt 1, Apr. 1994 should be justified separately. In slabs over 200 mm, if vc 1 000
0,8 0,7
5.3.2.3 Stress limitations at transfer for beams (SLS) 5.3.2.3.1 Compressive stresses Design compressive stresses in the concrete at transfer should not exceed 0,45fci at the extreme fibre (in the case of triangular or near triangular distribution of prestress) or 0,3fci for near uniform distribution of prestress, where fci is the concrete strength at transfer. 5.3.2.3.2 Tensile stresses in flexure Design tensile stresses in flexure in the concrete at transfer should not exceed the values given below: a) class 1 elements: ensure that at transfer, the tensile stress does not exceed the value of 1 MPa; b) class 2 elements: ensure that the tensile stress does not exceed the value appropriate to the concrete strength at transfer given in table 30; ensure that elements with pre-tensioned tendons have some tendons or unstressed reinforcement well distributed throughout the tensile zone of the section and elements with post-tensioned tendons have unstressed reinforcement located near the tension face of the element; c) class 3 elements (see also annex A): the tensile stress should, in general, not exceed the appropriate value for a class 2 element; where this stress is exceeded, regard the section in design as cracked.
5.3.3 Ultimate limit state for beams in flexure 5.3.3.1 Section analysis When analysing sections under maximum design loads, make the following assumptions:
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SABS 0100-1 Ed. 2.2 a) the strain distribution in the concrete in compression is derived from the assumption that plane sections remain plane; b) the stresses in the concrete in compression are either derived from the stress strain curve given in figure 1, with a γm of 1,5, or are taken as equal to 0,45fcu over the whole compression zone (see figure 4); in both cases, the strain at the outermost compression fibre is taken as 0,0035; c) the tensile strength of the concrete is ignored; d) the strains in bonded prestressing tendons and in any unstressed reinforcement, whether in tension or in compression, are derived from the assumption that plane sections remain plane; e) the stresses in bonded prestressing tendons, whether initially tensioned or untensioned, and in unstressed reinforcement are derived from the appropriate stress/strain curves; NOTE - The stress/strain curves for prestressing reinforcement are given in figure 3 and those for reinforcement are given in figure 2. An empirical approach towards obtaining the stress in the tendons at failure is given in 5.3.3.2.
f) in post-tensioned elements where the tendons are unbonded, the stress in the tendons does not exceed the values given in table 33 unless a higher stress can be justified on the basis of tests. Table 32 - Conditions at the ultimate limit state for rectangular beams with pre-tensioned tendons or with post-tensioned tendons having an effective bond 1
fpu Aps
2
3
4
5
6
7
Design stress in tendons as a proportion of the design strength fpb /0,87fpu
Ratio of depth of neutral axis to that of the centroid of the tendons in the tension zone x/d
fpe /fpu
fpe/fpu
fcu bd 0,6
0,5
0,05 0,10 0,15
1,0 1,0 0,99
1,0 1,0 0,97
0,20 0,25 0,30
0,92 0,88 0,85
0,35 0,40 0,45 0,50
0,83 0,81 0,79 0,77
0,4
0,6
0,5
0,4
1,0 1,0 0,95
0,11 0,22 0,32
0,11 0,22 0,31
0,11 0,22 0,31
0,90 0,86 0,83
0,88 0,84 0,80
0,40 0,48 0,55
0,39 0,47 0,54
0,38 0,46 0,52
0,80 0,77 0,74 0,71
0,76 0,72 0,68 0,64
0,63 0,70 0,77 0,83
0,60 0,67 0,72 0,77
0,58 0,62 0,66 0,69
5.3.3.2 Design formulae 5.3.3.2.1 In the absence of an analysis based on the assumptions given in 5.3.3.1, the moment of resistance of any shape of beam may be obtained from the following equation: Mu = fpbAps(d-dn) where
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SABS 0100-1 Ed. 2.2 Mu
is the design moment of resistance of beam;
fpb
is the design tensile stress in tendons at failure;
d
is the effective depth to centroid of steel area Aps;
dn
is the depth to centre of compression zone; and
Aps
is the area of prestressing tendons in tension zone.
5.3.3.2.2 For rectangular beams, and for flanged beams in which the compression block lies within the flange, dn = 0,45x, where x is the neutral axis depth. 5.3.3.2.3 Values for fpb and x may be derived from table 32 for pre-tensioned elements and for post-tensioned elements with effective bond between the concrete and tendons. The effective prestress after all losses shall be at least 0,45fpu. Ignore prestressing tendons and unstressed reinforcement in the compression zone in strength calculations when using this method. 5.3.3.2.4 For rectangular beams, and for flanged beams in which the neutral axis lies within the flange, the stress in the tendons at failure may be derived from table 33 for unbonded tendons. Table 33 - Conditions at the ultimate limit state for post-tensioned rectangular beams having unbonded tendons 1
fpe Aps fcu bd
2
3
4
Stress in tendons as a proportion of effective prestress fpb/fpe for values of effective span l effective depth d
5
6
7
Ratio of depth of neutral axis to that of the centroid of the tendons in the tension zone x/d for values of effective span l effective depth d
0,025 0,05 0,10
1,23 1,21 1,18
1,34 1,32 1,26
1,45 1,45 1,45
0,10 0,16 0,30
0,10 0,16 0,32
0,10 0,18 0,36
0,15 0,20
1,14 1,11
1,20 1,16
1,36 1,27
0,44 0,56
0,46 0,58
0,52 0,64
5.3.3.2.5 In table 32, the following assumptions have been made: a) the effective prestress after all losses have occurred (fpe) does not exceed 0,6fpu; b) the compression block is rectangular with a uniform stress of 0,45fcu; c) either the tendons are in ducts or, if they are free (as in hollow beams), diaphragms are provided to prevent a reduction of the effective depth; and d) the effective depth is determined by assuming that the tendons are in contact with the top of the duct or with the soffit of the diaphragms. 5.3.3.2.6 In addition, for unbonded tendons, values of f pb and x may be obtained from equations (15) and (16). (The value of fpb should not be taken as exceeding 0,7fpu.)
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SABS 0100-1 Ed. 2.2
fpb = fpe +
x = 2,47
7 000 le /d
1 & 1,7
f pu Aps
f pb
f cu bd
f pu
f pu Aps f cu bd
d
(15)
(16)
where fpb, Aps and d are as in 5.3.3.2.1; fpe
is the design effective prestress in tendons after all losses have occurred;
fpu
is the characteristic strength of tendons (see 5.1.5);
fcu
is the characteristic strength of concrete (see 5.1.5);
b
is the width or effective width of the section or flange in compression zone; and
le
is the length (see following paragraph).
Equation (15) has been derived by taking the length of the zone of inelasticity within the concrete as 10x. The length le should normally be taken as the length of the tendons between end anchorages. In the case of continuous multispan beams, this length may be determined as in figure 26.
Figure 26 — Determination of le 5.3.3.3 Non-rectangular beams Non-rectangular sections may be analysed using the assumptions given in 5.3.3.1 or the design formulae given in 5.3.3.2.
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SABS 0100-1 Ed. 2.2 5.3.3.4 Unstressed reinforcement in the tension zone In the absence of a rigorous analysis, the area of reinforcement As may be replaced by an equivalent area of prestressing tendons Asfy /fpu.
5.3.4 Shear resistance of beams Calculation for shear resistance is only required for the ultimate limit state. The provisions of this subclause apply to class 1, class 2, and class 3 prestressed concrete elements. Consider the ultimate shear resistance of the concrete alone, Vc, at both sections, uncracked (see 5.3.4.2) and cracked (see 5.3.4.3) in flexure. Take the lower value and, if necessary, provide shear reinforcement (see 5.3.4.4). 5.3.4.1 Maximum shear stress Under no circumstances should the maximum design shear stress v exceed the lesser of 0,75 f cu or 4,75 MPa (this includes an allowance for a γm of 1,40). 5.3.4.2 Sections uncracked in flexure 5.3.4.2.1 The ultimate shear resistance of a section uncracked in flexure, Vco, corresponds to the occurrence of a maximum design principal tensile stress at the centroidal axis of the section ft = 0,23 f cu 5.3.4.2.2 In the calculation of Vco, take the value of prestress at the centroidal axis as 0,8fcp. The value of Vco is given by Vco = 0,67 bh f t² 0,8 f cp f t
(17)
where ft
= 0,23 f cu , taken as positive;
fcp
is the design compressive stress at the centroidal axis due to prestress, taken as positive;
b
is the width of beam, which, for T-beams, I-beams and L-beams, is replaced by the width of rib, bw; and
h
is the overall depth of beam.
Table 34 gives values of Vco /bh obtained from equation (17) for different concrete grades and applicable values of fcp.
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SABS 0100-1 Ed. 2.2 Table 34 Values of Vco /bh 1
2
3
4
5
Vco /bh fcp
MPa
MPa
Concrete grade 30
40
50
60
2
1,27
1,41
1,54
1,64
4
1,59
1,74
1,90
2,00
6
1,85
2,02
2,17
2,12
8
2,08
2,26
2,42
2,56
10
2,29
2,48
2,65
2,80
14
2,65
2,87
3,06
3,22
5.3.4.2.3 In flanged beams where the centroidal axis occurs in the flange, limit the principal tensile the stress ft to 0,23 f cu at the intersection of the flange and web. When calculating Vco, use 0,8 of Amdt 1, Apr. 1994 stress due to prestress at this intersection. 5.3.4.2.4 For a section uncracked in flexure and with inclined tendons or compression zones, the component of prestressing force or that of compression force normal to the longitudinal axis of the beam may be added to Vco. 5.3.4.2.5 In a pre-tensioned beam, the critical section should be taken at a distance from the edge of the bearing equal to the height of the centroid of the section above the soffit. Where this section occurs within the prestressed development length, the compressive stress at the centroidal axis due to prestress to be used in equation 17 may be calculated from the following relationship: fcpx =
x lp
2 &
x lp
fcp
where fcp is the design stress at the end of the prestress development length lp. The prestress development length lp should be taken as the greater of the transmission length (see 5.8.4) or the overall depth of the element. 5.3.4.3 Sections cracked in flexure 5.3.4.3.1 Calculate the design ultimate shear resistance Vcr of a section cracked in flexure, using the following equation: Vc r ' 1 & 0,55
fp e f pu
vc bd % Mo
V M
(18)
where
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SABS 0100-1 Ed. 2.2 d
is the distance from extreme compression fibre to centroid of steel area (Aps + As) in tension zone;
Mo
is the moment necessary to produce zero stress in concrete at the extreme tension fibre; and
Mo
is equal to 0,8 f pt
Ι
Yt
;
where Yt
is the distance from the centroid of the concrete section to the extreme tension fibre;
fpt
is the stress at the extreme tension fibre due to prestress only;
I
is the second moment of area; and
fpe
is the design effective prestress in tendons after all losses have occurred (should not be taken as exceeding 0,6 fpu).
NOTE ) Where the steel area in the tension zone consists of tendons and reinforcement, fpe may be taken as the value obtained by dividing the effective prestressing force by an equivalent area of tendons equal to
Aps % As
fy f pu
where fpu
is the characteristic strength of tendons (see 5.3.3.2 or figure 3);
vc
is the maximum design shear resistance of the concrete (the value obtainable from 4.3.4);
V and M are the design shear force and bending moment, respectively, at the section under consideration, and due to the particular ultimate load condition; and b
is the width or effective width of rectangular section or the width of the rib.
The value of Vcr should be taken as at least 0,1bd f cu . 5.3.4.3.2 The value of Vcr at a particular section, calculated using equation (18), may be assumed to be constant for a distance equal to d/2, measured in the direction of increasing moment, from that particular section. 5.3.4.3.3 For a section cracked in flexure and with inclined tendons or compression cords, the design shear forces produced should be combined with the external design load effects where these effects are increased. 5.3.4.4 Shear reinforcement 5.3.4.4.1 When V, the shear force due to the design ultimate loads, is less that Vc, which is the shear force that can be carried by the concrete, shear reinforcement need not be provided in the following cases: a) where V is less than 0,5 Vc;
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SABS 0100-1 Ed. 2.2 b) in elements of minor importance; and c) where tests carried out in accordance with 3.4.5 have shown that shear reinforcement is not required. 5.3.4.4.2 In all cases except those in 5.3.4.4.1, minimum shear reinforcement in the form of links should be provided such that Asv sv
0,4b 0,87 f yv
where fyv
is the characteristic strength of the reinforcement (but not more than 450 MPa);
b
is as in equation (18);
Asv
is the cross-sectional area of the two legs of a link; and
sv
is the link spacing along length of beam.
5.3.4.4.3 When V, the shear force due to the design ultimate loads, exceeds Vc, ensure that the shear reinforcement provided in addition is such that Asv sv
V Vc 0,87 f yv dt
where dt is taken as the depth from the extreme compression fibre, to the greater of either the longitudinal bars (tendons, group of tendons) or the centroid of the tendons. 5.3.4.5 Arrangement of shear reinforcement 5.3.4.5.1 In rectangular beams, at both corners in the tensile zone, a link should pass round a longitudinal bar, a tendon or a group of tendons having a diameter not less than the link diameter. A link should extend as close to the tension or compression faces as possible, with due regard to cover. Ensure that the links provided at a cross-section enclose all the tendons and unstressed reinforcement provided at the cross-section and that they are adequately anchored (see 4.11.6.4). 5.3.4.5.2 Ensure that the spacing of links along a beam does not exceed 0,75dt or four times the web thickness for flanged beams. When V exceeds 1,8Vc, reduce the maximum spacing to 0,5dt. Ensure that the lateral spacing of the individual legs of the links provided at a cross-section does not exceed 0,75dt.
5.3.5 Torsional resistance of beams In general, when it is considered that torsional resistance or stiffness of beams need not be taken into account in the analysis of the structure, no specific calculations for torsion will be necessary, adequate control of any torsional cracking being provided by the required nominal shear reinforcement. Calculations are required when torsional resistance is necessary for equilibrium or when significant torsional stresses may occur. The method for reinforced concrete beams given in 4.3.5 may generally be used.
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SABS 0100-1 Ed. 2.2 5.3.6 Deflection of beams NOTE - See also annex A.
5.3.6.1 Class 1 and class 2 elements (see 3.2.3.3.1.2) 5.3.6.1.1 The instantaneous deflection due to service loads may be calculated with the use of elastic analysis based on the concrete section properties and on the value for the modulus of elasticity given in 3.4.2.1. 5.3.6.1.2 The total long-term deflection due to the prestressing force, self-weight load and any sustained imposed load may be calculated with the use of elastic analysis based on the concrete section properties and on an effective modulus of elasticity based on the creep of the concrete per unit length for unit applied stress after the period under consideration (specific creep). The values for specific creep given in 5.8.2.5 may in general be used unless a more accurate assessment is required. Make due allowance for the loss of prestress after the period under consideration. Ensure that the deflections comply with the limits given in 3.2.3.2. 5.3.6.2 Class 3 elements Where the permanent load is less than or equal to 25 % of the imposed load, the deflection of class 3 elements may be calculated in accordance with 5.3.6.1. Where the permanent load exceeds 25 % of the imposed load, the basic span/effective depth ratios given in 4.3.6 and table 10 should be complied with unless more rigorous calculations based on the moment curvature relationship are made.
5.4 Slabs The provisions given in 5.3 for beams apply also to slabs. The methods of analysis given in 4.4.2 and 4.5.2 are appropriate for the ultimate limit state. Elastic analysis should be used for the serviceability limit states. The design for shear should be in accordance with 5.3.4 except that shear reinforcement need not be provided if v is less than vc. The analysis and design of flat slabs should be carried out in accordance with appropriate specialist literature.
5.5 Columns Prestressed concrete columns in framed structures, where the mean stress in the concrete section imposed by the tendons is less than 2,5 MPa, may be analysed as reinforced columns in accordance with 4.7.
5.6 Tension members The tensile strength of tension members should be based on the design strength of the prestressing tendons (0,87fpu) and the strength developed by any unstressed reinforcement. The unstressed reinforcement may usually be assumed to be acting at its design stress (0,87fy); in special cases it may be necessary to check the stress in the reinforcement, using strain compatibility.
5.7 Low density aggregate prestressed concrete Design of members in low density aggregate prestressed concrete should be based on the provisions given in 4.12. For assessment of the prestress losses, which will, in general, exceed those for dense aggregate concrete, specialist literature should be consulted.
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SABS 0100-1 Ed. 2.2 5.8 Prestressing 5.8.1 Maximum initial prestress 5.8.1.1 The jacking force should not normally exceed 75 % of the characteristic strength of the tendon but may be increased to 80 %, provided that additional consideration is given to safety, to the stress/strain characteristics of the tendon, and to the assessment of the friction losses. 5.8.1.2 In the determination of the jacking force to be used, consideration should also be given to the gripping efficiency of the anchorage. 5.8.1.3 When deflected tendons are used in pre-tensioning, consideration should, in the determination of the maximum initial prestress, be given to the possible influence of the size of the deflector on the strength of the tendons. (See the appropriate clause of SABS 0100-2.) Attention should also be paid to the effect of any frictional forces that may occur.
5.8.2 Loss of prestress other than frictional losses 5.8.2.1 General When calculating the forces in tendons at the various stages considered in design, make allowance for the appropriate losses of prestress resulting from a) relaxation of steel of the tendons, b) the elastic deformation and subsequent shrinkage and creep of the concrete, c) slip or movement of tendons at anchorages during anchoring, and d) other causes in special circumstances, for example when steam curing is used with pre-tensioning. If experimental evidence on performance is not available, take the properties of the steel and of the concrete into account when calculating the losses of prestress from these causes. The provisions given in the following subclauses are applicable to a wide range of structures, especially buildings. It must be recognized, however, that these recommendations are necessarily general and approximate. 5.8.2.2 Loss of prestress due to relaxation of steel 5.8.2.2.1 Ensure that the loss of force in the tendon allowed for in the design is double the maximum relaxation after 1 000 h duration, for a jacking force equal to that imposed at transfer. 5.8.2.2.2 When there is no experimental evidence available, the relaxation loss for normal stress-relieved wire or strand may be assumed to decrease linearly from 10 % for an initial prestress of 80 %, to 3 % for an initial prestress of 50 %. This would apply when the estimated total creep and shrinkage strain of the concrete is less than 500 x 10-6. When the creep plus shrinkage strain exceeds 500 x 10-6, the loss for an initial stress of 80 % should be reduced to 8,5 %. Losses for low-relaxation tendons may be assumed to be half the above values. 5.8.2.2.3 Make no reduction in the value of the relaxation loss for a tendon when a load equal to or exceeding the relevant jacking force has been applied for a short time prior to the anchoring of the tendon. 5.8.2.2.4 In special cases, such as tendons exposed to high temperatures or subjected to large lateral loads, greater relaxation losses will occur. Consult specialist literature in these cases.
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SABS 0100-1 Ed. 2.2 5.8.2.3 Loss of prestress due to elastic deformation of the concrete 5.8.2.3.1 Calculation of the immediate loss of force in the tendons due to elastic deformation of the concrete at transfer may be based on the values for the modulus of elasticity of the concrete given in table 1 when the actual experimental values are not available (see annex C). The modulus of elasticity of the tendons may be obtained from 3.4.2.3. 5.8.2.3.2 For pre-tensioning, calculate the loss of prestress in the tendons at transfer on a modular ratio basis, using the stress in the adjacent concrete. 5.8.2.3.3 For elements with post-tensioning tendons that are not stressed simultaneously, there is a progressive loss of prestress during transfer, due to the gradual application of the prestressing force. Calculate the resulting loss of prestress in the tendons on the basis of half the product of the modular ratio and the stress in the concrete adjacent to the tendons averaged along their length; alternatively, the loss of prestress may be accurately calculated by basing it on the sequence of tensioning. 5.8.2.3.4 In making these calculations, it may usually be assumed that the tendons are located at their centroid. 5.8.2.4 Loss of prestress due to shrinkage of the concrete 5.8.2.4.1 The shrinkage strain to be considered depends upon the following: a) the aggregate used; b) the original water content; c) the effective age of transfer; d) the effective section thickness; and e) the ambient relative humidity. 5.8.2.4.2 The loss of prestress in the tendons due to shrinkage of the concrete may be calculated as the product of the shrinkage per unit length of the concrete (see table 35) and the modulus of elasticity of the tendons (as in 3.4.2.3).
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SABS 0100-1 Ed. 2.2 Table 35 - Shrinkage of concrete 1
2
3
4
Shrinkage per unit length Relative humidity 80 %
60 %
35 %
e.g. coastal towns
e.g. most inland areas
e.g. environments of unusually low relative humidity such as Windhoek and Upington
Pre-tensioning Transfer at 3 d to 5 d after concreting
180 x 10-6
310 x 10-6
420 x 10-6
Post-tensioning Transfer at 7 d to 14 d after concreting
140 x 10-6
250 x 10-6
350 x 10-6
System
5.8.2.4.3 Some adjustment to the figures in table 35 will be necessary for other ages of concrete at transfer, for other conditions of exposure, or for massive structures, in which cases specialist literature should be consulted. 5.8.2.4.4 When it is necessary to determine the loss of prestress and the deformation of the concrete at some stage before the total shrinkage is reached, it may be assumed that half the total shrinkage takes place during the first month after transfer and that three-quarters of the total shrinkage takes place within the first 6 months after transfer. 5.8.2.4.5 In certain regions of South Africa, the aggregate may exhibit abnormally high shrinkage characteristics. The fine-grained shales and sandstones of the Beaufort group of the Karoo sequence are those most likely to lead to high dimensional changes in concrete. Seek advice when these aggregates or others of a similar type are to be used. 5.8.2.5 Loss of prestress due to creep of the concrete 5.8.2.5.1 The loss of prestress in the tendons may be calculated on the assumption that creep is proportional to the stress in the concrete (see 5.8.2.5.4). The loss of prestress is obtained as the product of the creep per unit length of the concrete adjacent to the tendons and the modulus of elasticity of the tendons (see 3.4.2.3). When calculating this loss, it is usually sufficient to assume that the tendons are located at their centroid. 5.8.2.5.2 For pre-tensioning at between 3 d and 5 d after concreting and for humid or dry conditions of exposure where the required cube strength at transfer exceeds 40,0 MPa, take the creep of the concrete per unit length as 48 x 10-6 per megapascal. For lower values of cube strength at transfer, assume the creep per unit length to be 48 x 10-6 x 40,0/fci per megapascal, where fci is the concrete strength at transfer. 5.8.2.5.3 For post-tensioning at between 7 d and 14 d after concreting and for humid or dry conditions of exposure where the required cube strength at transfer exceeds 40,0 MPa, take the creep of the concrete per unit length as 36 x 10-6 per megapascal. For lower values of cube strength at transfer, take the creep per unit length as 36 x 10-6 x 40,0/fci per megapascal. 5.8.2.5.4 The values as in 5.8.2.5.2 and 5.8.2.5.3 are applicable when the maximum stress anywhere
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SABS 0100-1 Ed. 2.2 in the section at transfer is less than one-third of the cube strength of concrete. Where the maximum stress anywhere in the section at transfer exceeds one-third of the cube strength of the concrete, the value for the creep per unit length should be increased up to the maximum value equal to 1,25 times the values given in 5.8.2.5.2 and 5.8.2.5.3, as relevant. This maximum value is applicable when the maximum stress at transfer is half the cube strength. For intermediate stresses, the values for the creep per unit length should be interpolated linearly. 5.8.2.5.5 The values in the preceding subclauses relate to the ultimate creep after a period of years. When it is necessary to determine the deformation of the concrete due to creep at some earlier stage, it may be assumed that half the total creep takes place in the first month after transfer and that threequarters of the total creep takes place in the first 6 months after transfer. 5.8.2.5.6 When applying the provisions given above, which are necessarily general, consult specialist literature for more detailed information on the factors affecting creep, particularly those such as aggregates used, original water content, effective age at transfer, effective section thickness, ambient relative humidity and ambient temperature. Care should be taken when using Reef quartzite, aggregates of the Beaufort group of the Karoo sequence and the Lesotho basalts, since the values may be three times bigger. (See also figure C.1.) 5.8.2.6 Draw-in during anchorage In post-tensioning systems, make allowance for any movement of the tendon at the anchorage when the prestressing force is transferred from the tensioning equipment to the anchorage. The loss due to this movement is particularly important in short elements and for such elements check, on site, the allowance made by the designer. 5.8.2.7 Loss of prestress due to steam curing Where steam curing is used in the manufacture of prestressed concrete elements, consider changes in the behaviour of the material at temperatures higher than normal.
5.8.3 Loss of prestress due to friction 5.8.3.1 General 5.8.3.1.1 In post-tensioning systems, there will be movement of the greater part of the tendon relative to the surrounding duct during the tensioning operation and, if the tendon is in contact with either the duct or any spacers provided, friction will cause a reduction in the prestressing force as the distance from the jack increases. In addition, a certain amount of friction will be developed in the jack itself and in the anchorage through which the tendon passes. 5.8.3.1.2 In the absence of evidence established to the satisfaction of the engineer, assess, in accordance with 5.8.3.2 to 5.8.3.4, the stress variation likely to be expected along the design profile in order to obtain the prestressing force at the critical sections considered in design. Calculate the extension of the tendon, allowing for the variation in tension along its length. 5.8.3.2 Friction in the jack and anchorage This will vary considerably between systems and should be ascertained for the type of jack and the anchorage system to be used. 5.8.3.3 Friction in the duct due to unintentional variation from the specified profile Whether the desired duct profile is straight or curved or a combination of both, there will be slight variations in the actual line of the duct, which may cause additional points of contact between the
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SABS 0100-1 Ed. 2.2 tendon and the sides of the duct, and so produce friction. Calculate the prestressing force Px at any distance x from the jack, from the following equation: Px = Poe-Kx (where Kx < 0,2, take e-Kx as 1 - Kx) where Po is the prestressing force in tendon at jacking end; e
is the base of Napierian logarithms (2,718); and
K
is the constant depending on the type of duct or sheath employed, the nature of its inside surface, the method of forming it, and the degree of vibration employed in placing the concrete.
Take the value of K per metre of length in the above formula as at least 33 x 10-4 but a) K = 17 x 10-4 where strong rigid sheaths or duct formers are used so closely supported that they are not displaced during the concreting operation; and b) K = 25 x 10-4 for greased strands running in plastics sleeves. Other values may be used, provided they have been established by tests to the satisfaction of the engineer. 5.8.3.4 Friction in the duct due to curvature of the tendon 5.8.3.4.1 When a tendon is curved, the loss of tension due to friction is dependent on the angle the tendon is turned through and on the coefficient of friction µ between the tendon and its supports. 5.8.3.4.2 Calculate the prestressing force Px at any distance x along the curve from the tangent point from the following equation: Px = Poe
-µx/rps
where Po is the prestressing force in the tendons at tangent point near jacking end; rps is the radius of curvature; and e
is as defined in 5.8.3.3.
Values of µ may be taken as follows: a) 0,55 for lightly rusted strand running in an unlined concrete duct; b) 0,30 for lightly rusted strand or wire running in a lightly rusted steel duct; c) 0,25 for strand or wire running in a steel duct; d) 0,17 for pulled-through oversized duct oiled with water-soluble oil; and
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SABS 0100-1 Ed. 2.2 e) 0,05 for greased strand running in plastics sleeve.
5.8.4 Transmission length in pre-tensioned elements 5.8.4.1 The transmission length is defined as the length of the element required to transmit the initial prestressing force in a tendon to the concrete. 5.8.4.2 The transmission length depends on a number of variables, the most important being a) the degree of compaction of the concrete, b) the size and type of tendon, c) the strength of the concrete, and d) the deformation, e.g. crimp of the tendon and surface condition of the tendon. 5.8.4.3 The transmission length can vary a great deal for different factory or site conditions, for example it has been shown that the transmission length for wire can vary between 50 and 160 wire diameters. As far as possible, therefore, the engineer should base the transmission length on experimental evidence for known site or factory conditions. 5.8.4.4 Consider the following general provisions, based on research, in relation to the known site or factory conditions: a) for factory-produced units where plain or indented wire with a small offset crimp (e.g. 0,3 mm offset, 40 mm pitch) is used, a transmission length of 100 wire diameters may be assumed when the ends of the units are fully compacted and the cube strength of the concrete at transfer is at least 35 MPa; b) for units where wire of a considerable crimp (e.g. 1,0 mm offset, 40 mm pitch) is used, a transmission length of 65 wire diameters may be assumed when the ends of the units are fully compacted and the cube strength of the concrete at transfer is at least 35 MPa; c) the development of stress from the end of the unit to the point of maximum stress is such that it may be assumed that 80 % of the maximum stress is developed in a length of 70 wire diameters for the conditions described in (a) above, and in a length of 54 wire diameters for the conditions described in (b) above; d) when the cube strength of the concrete at transfer is less than 35 MPa, the transmission lengths may be greater; e) the transmission length for tendons near the top of a beam may exceed that for identical tendons placed lower in the beam, since the concrete near the top is less likely to be as well compacted; f) since the sudden release of tendons leads to a great increase in the transmission lengths in the units near the releasing end of the bed, tendons shall be so cut as not to cause a sudden shock to the concrete; g) from the available experimental data, the transmission length for small diameter strand is not proportional to the diameter of the tendon, nor is the scatter of results as great as it is for wire; table 36 gives values for the transmission lengths for small diameter strand; in the absence of more exact data, these values may be used in design. h) if the tendons are prevented from bonding to the concrete near the ends of the elements by the use
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SABS 0100-1 Ed. 2.2 of sleeves or tape, the values given in table 36 for the transmission length may be used, the assumption being that the transmission zone starts at the point where the debonding process has been stopped. Table 36 - Transmission lengths for small diameter strand 1
2
Diameter of strand
Transmission length l t mm
mm 9,3 12,5 15,0
465 625 750
5.8.4.5 Alternatively, for calculating the transmission length lt, in the absence of experimental evidence, the following equation may be used for initial prestressing forces of up to 75 % of the characteristic strength of the tendon, when the ends of the elements are fully compacted: lt =
Kt
f ci
where
is the nominal diameter of tendon;
fci
is the concrete strength at transfer; and
Kt is a coefficient for type of tendon, which is selected from the following: a) plain or indented wire (including crimped wire with a small wave height): Kt = 600; b) crimped wire with a total wave height of at least 0,15
: K = 400; t
c) 7-wire standard or super strand: Kt = 240; and d) 7-wire drawn strand: Kt = 360.
5.8.5 End blocks in prestressed elements 5.8.5.1 General For the design of end blocks, attention is drawn to the following: a) reinforcement shall be provided where required in tendon anchorage zones to resist bursting, splitting, and spalling forces induced by tendon anchorages. Regions of abrupt change in section shall be adequately reinforced; b) end blocks shall be provided where required for support bearing or for distribution of concentrated prestressing forces; c) post-tensioning anchorages and supporting concrete shall be designed to resist the maximum
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SABS 0100-1 Ed. 2.2 jacking force for the strength of concrete at the time of prestressing; and d) post-tensioning anchorage zones shall be designed to develop the guaranteed ultimate strength of the lesser of prestressing anchorages or prestressing tendons. 5.8.5.2 Bursting tensile forces in post-tensioned elements 5.8.5.2.1 The bursting forces round individual anchorages should be assessed in the end blocks on the basis of the tendon jacking load (for serviceability limit state) or the nominal tendon force (for ultimate limit state). The latter is necessary only in the case of elements with unbonded tendons. For elements with rectangular anchorages and for rectangular end blocks, the bursting tensile force Fbst may be calculated from table 37 in relation to the value of Ypo/Yo for each direction, where Yo
is half the side of the end block;
Ypo
is half the side of the loaded area; and
Pk
is the tendon jacking force.
Circular bearing plates should be treated as square plates of equivalent area. Table 37 - Design bursting tensile forces in end blocks 1
2
Ypo/Yo
Fbst/Pk
0,2 0,3 0,4
0,23 0,23 0,20
0,5 0,6 0,7
0,17 0,14 0,11
NOTE - Intermediate values may be interpolated.
5.8.5.2.2 This force, Fbst, will be distributed in a region extending from 0,2 Yo to 2,0 Yo from the loaded face and should be resisted by reinforcement in the form of spirals or closed links, uniformly distributed thoughout this region. The reinforcement should act at a stress of 200 MPa (in the case of serviceability limit state) or at its design strength, i.e. 0,87fy (in the case of ultimate limit state). When the concrete cover to the reinforcement is less than 50 mm, the stress shall be limited to a value corresponding to a strain of 0,001. 5.8.5.2.3 Where groups of anchorages or bearing plates are used, the end block should be divided into a series of symmetrically loaded prisms, and each prism should be treated in the above manner. However, additional reinforcement will be required round the groups of anchorages to ensure overall equilibrium of the end block. 5.8.5.2.4 Special attention should also be paid to end blocks having a cross-section different in shape from that of the general cross-section of the beam. Specialist literature should be consulted. 5.8.5.2.5 Compliance with the above requirements will generallly ensure that bursting tensile forces along the load axis are provided for. Alternative methods of design that make allowance for the tensile
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SABS 0100-1 Ed. 2.2 strength of the concrete may be used, in which case specialist literature should be consulted.
5.9 Considerations affecting design details 5.9.1 General The following subclauses supplement the considerations for design details for reinforced concrete as given in 4.11.
5.9.2 Size and number of prestressing tendons 5.9.2.1 Ensure that the size and number of prestressing tendons are such that cracking of the concrete would precede failure of the beam. 5.9.2.2 This requirement will be satisfied for under-reinforced beams, where failure would be due to fracture of the tendons, if the percentage of reinforcement, calculated on an area equal to the width of the beam soffit multiplied by its overall depth, is at least 0,15. For over-reinforced beams, where failure would be due to crushing of the concrete, the maximum number and size of tendons will be governed by considerations of strain compatibility (see 5.3.3.1).
5.9.3 Cover to prestressing tendons 5.9.3.1 General Cover to prestressing tendons will generally be governed by considerations (see SABS 0100-2) and fire resistance.
of durability
5.9.3.2 Bonded tendons The recommendations of 4.11.2 concerning cover to reinforcement may also be applicable to tendons. The required nominal cover against corrosion and the associated mix limitations are given in SABS 0100-2. The values of cover as fire protection for various structural elements may be taken from table 38. The ends of individual pre-tensioned tendons do not normally require concrete cover and should preferably be cut off flush with the end of the concrete element.
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SABS 0100-1 Ed. 2.2 Table 38 - Nominal cover to all steel to meet specified periods of fire resistance 1
2
3
4
5
6
7
Nominal cover Fire resistance h
mm Beams
Floors
Ribs
Simply supported
Continuous
Simply supported
Continuous
Simply supported
Continuous
0,5
20
20
20
20
20
20
1
20
20
25
20
35
20
1,5
35
20
30
25
45
35
2
60
35
40
35
55
45
3
70
60
55
45
65
55
4
80
70
65
55
75
65
NOTES 1 For the purposes of assessing a nominal cover for beams, the cover to main bars, which would have been obtained from table 43, has been reduced by a notional allowance for stirrups of 10 mm to cover the range 8 mm to 12 mm. 2 The nominal covers given relate specifically to the minimum element dimensions (see clause 7). Increased covers are necessary if smaller elements are used. (Specialist literature should be consulted.) 3 Cases that lie below the line require attention to the additional measures necessary to reduce the risks of spalling (see clause 7).
5.9.3.3 Cover to tendons in ducts The cover to any duct should be at least the greater of 50 mm or the diameter of the duct. Precautions should be taken to ensure a dense concrete cover, particularly with large or wide ducts. 5.9.3.4 Cover to external tendons Where the tendons are located outside the structural concrete (as defined in the relevant clause of SABS 0100-2) and are to be protected by dense concrete added subsequently, the thickness of this cover shall be at least equal to that required for tendons inside the structural concrete under similar conditions. The concrete cover should be anchored by reinforcement to the prestressed element, and should be checked for crack control in accordance with clause 4. 5.9.3.5 Cover to curved tendons For cover to curved tendons, see 5.9.5.2.
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SABS 0100-1 Ed. 2.2 5.9.4 Spacing of prestressing tendons 5.9.4.1 General In all prestressed elements, there should be sufficient gaps between the tendons or groups of tendons to allow the largest size of aggregate used to move, under vibration, to all parts of the mould. 5.9.4.2 Spacing of bonded tendons The provisions of 4.11.8 concerning spacing of reinforcement apply. In pre-tensioned elements, where anchorage is achieved by bond, the spacing of the wires or strands in the ends of the elements should be such as to allow the transmission length given in 5.8.4 to develop. In addition, if the tendons are positioned in two or more widely spaced groups, the possibility of longitudinal splitting of the element should be considered. 5.9.4.3 Spacing of tendons in ducts The clear distance between ducts or between ducts and other tendons should be not less than the greatest of the following: a) hagg + 5 mm, where hagg is the nominal maximum size of the coarse aggregate; b) in the vertical direction, the vertical internal dimension of the duct; or c) in the horizontal direction, the horizontal internal dimension of the duct. Where internal vibrators are used, sufficient space should be provided between ducts to enable the vibrator to be inserted. Where two or more rows of ducts are used, the horizontal gaps between the ducts should be vertically in line wherever possible, for ease of construction. 5.9.4.4 Spacing of curved tendons For spacing of curved tendons, see 5.9.5.3.
5.9.5 Curved tendons 5.9.5.1 General Where curved tendons are used in post-tensioning, the positioning of the tendon ducts and the sequence of tensioning should be such as to prevent a) bursting of the cover at the sides of ducts in thin elements, b) bursting of the cover where the tendons run close to and approximately parallel with the soffit of the element, and c) crushing of the concrete that separates tendons in the same vertical plane. (If necessary, provide reinforcement between ducts.) 5.9.5.2 Cover to curved tendons In order to prevent bursting of the cover perpendicular to the plane of curvature, and in the plane of curvature, the cover should be in accordance with the values given in table 39.
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SABS 0100-1 Ed. 2.2 Where the curved tendons run close to, and approximately parallel with, the surface of an element and if the tendons develop radial forces perpendicular to the exposed surface of the concrete, the duct, if necessary, should be restrained by stirrup reinforcement anchored into the element. Table 39 - Minimum cover to curved ducts 1
2
3
4
5
6
7
8
9
10
80
90
100
Minimum cover mm Radius of curvature of duct
Duct internal diameter mm 19
30
40
50
m
60
70
Tendon force kN
2 4 6
296
387
960
1337
1920
2640
3360
4320
5183
50
55 50
155 70 50
220 100 65
320 145 90
445 205 125
265 165
350 220
420 265
55 50
75 65 60
95 85 75
115 100 90
150 120 110
185 140 125
70
85 80
100 95 90
115 110 105
8 10 12 14 16 18 20 40
100 50
50
50
50
60
70
80
90
100
NOTES 1 The tendon force shown is the maximum normally available for the given size of duct (taken as 80 % of the characteristic strength of the tendon). 2 Where tendon profilers or spacers are provided in the ducts, and these are of a type that will concentrate the radial force, the values given in the table will need to be increased. 3 The cover for a given combination of duct internal diameter and radius of curvature shown in the table may be reduced in proportion to the square root of the tendon force when this is less than the value tabulated, subject to the provisions of 5.9.3.3 and 5.9.3.4.
5.9.5.3 Spacing of curved tendons In order to prevent crushing of the concrete that separates the ducts, the minimum spacing between ducts should be as follows: a) in the plane of curvature: the distance given in table 40; and b) perpendicular to the plane of curvature: the distance given in 5.9.4.3.
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SABS 0100-1 Ed. 2.2 Table 40 - Minimum distance between centre-lines of ducts in plane of curvature 1
2
3
4
5
6
7
8
9
10
Minimum distance between centre-lines of ducts in plane of curvature mm Radius of curvature of duct
Duct internal diameter mm 19
30
40
50
m
60
70
80
90
100
Tendon force kN
2 4 6
296
387
960
1337
1920
2640
3360
4320
5183
110 55 38
140 70 60
350 175 120
485 245 165
700 350 235
960 480 320
610 410
785 525
940 630
90 80
125 100
175 140 60
240 195 160
305 245 205
395 315 265
470 375 315
140
175 160
225 195 180
270 235 210
140
160
180
200
8 10 12 14 16 18 20 40
38
60
80
100
120
NOTES 1 The tendon force shown is the maximum normally available for the given size of duct (taken as 80 % of the characteristic strength of the tendon). 2 Values less than 2 x the internal diameter of the duct are not included. 3 Where tendon profilers or spacers are provided in the ducts, and these are of a type that will concentrate the radial force, the values given in the table will need to be increased. If necessary, reinforcement should be provided between ducts. 4 The distance for a given combination of duct internal diameter and radius of curvature shown in the table may be reduced in proportion to the tendon force when this is less than the value tabulated, subject to the provisions of 5.9.4.3.
5.9.5.4 Special measures to reduce spacing of ducts As an exception, it may be possible first to tension and grout the tendon that has the least radius of curvature, and to allow an interval of 48 h to elapse before tensioning the next tendon. In this case, the provisions for spacing given in 5.9.4.3 apply.
5.9.6 Longitudinal reinforcement in prestressed concrete beams 5.9.6.1 Reinforcement may be used in prestressed concrete elements either to increase the strength of sections or to comply with 5.3.4.3.
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SABS 0100-1 Ed. 2.2 5.9.6.2 Ensure that any calculation that takes unstressed reinforcement into account will still be in accordance with 5.3.2.1 and 5.3.3.1. 5.9.6.3 Reinforcement may be necessary, particularly where post-tensioning systems are used, to control any cracking resulting from the restraint to longitudinal shrinkage of beams that is provided by the formwork during the time before the prestress is applied.
5.9.7 Links in prestressed concrete beams 5.9.7.1 The number and disposition of links in rectangular beams and in the webs of flanged beams will normally be governed by considerations of shear (see 5.3.4). 5.9.7.2 Provide links to resist the bursting tensile forces in the end blocks of prestressed beams in accordance with 5.8.5. 5.9.7.3 Provide links in the transmission length of pre-tensioned beams in accordance with the requirements of 5.3.4 and using the information given in 5.8.4.
5.9.8 Shock loading When a prestressed concrete beam may be required to resist shock loading, reinforce it with closed links and longitudinal reinforcement, preferably of mild steel. Other methods of design and detailing may be used, provided it can be shown that the beam can develop the required ductility.
6 Precast, composite and plain concrete constructions (design and detailing) 6.1 General 6.1.1 Design objectives This subclause is concerned with the additional considerations that arise in design and detailing when precast units, including large panels, are incorporated into a structure, or when a structure in its entirety is of precast concrete construction. It also covers the use of plain concrete for walls.
6.1.2 Limit states design 6.1.2.1 Basis of design The limit states philosophy set out in clause 3 also applies to precast in-situ construction and therefore, in general, the recommended methods of design and detailing for reinforced concrete given in clause 4 and those for prestressed concrete given in clause 5 also apply to precast and composite construction. Subsections in clauses 4 and 5 that do not apply are either specifically worded for in-situ construction or are modified by this clause. Provisions for the design and detailing of plain concrete walls are given in 6.5. 6.1.2.2 Handling stress Precast units should be designed to resist, without permanent damage, all stresses induced by handling, storage, transport and erection. (See also 5.3.1.2 and SABS 0100-2.)
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SABS 0100-1 Ed. 2.2 When necessary, specify the positions of lifting and supporting points. Consultation at the design stage with those responsible for handling is an advantage. Ensure that the design takes into account the effects of both snatch lifting from and placing onto supports. 6.1.2.3 Connections and joints 6.1.2.3.1 The design of connections is of fundamental importance in precast construction and should be carefully considered. The engineer responsible for the overall stability of the structure should ensure the compatibility of the design and details of components. The responsibility for overall stability shall be clearly assigned when some or all of the design and details are not worked out by the engineer. 6.1.2.3.2 Joints to allow for movement due to shrinkage, thermal effects and possible differential settlement of foundations are of as great importance in precast as in in-situ construction. Determine the number and spacing of such joints (see annex B) at an early stage in the design. In the design of beam and slab ends on corbels and nibs, take particular care to provide overlap and anchorage (in accordance with 4.11.6 and 4.11.7) of all reinforcement adjacent to the contact faces, taking constructional tolerances into consideration. 6.1.2.4 Stability 6.1.2.4.1 The provisions regarding stability given in 4.1.2 apply also to precast, composite and plain concrete construction except that, in structures of five storeys or more, supported by plain concrete walls, it will be necessary to ensure that the area of effective vertical ties from foundation to roof level is at least 0,2 % of the cross-sectional area of the walls. 6.1.2.4.2 The tie forces referred to in 4.1.2 should be resisted by reinforcement or prestressing tendons embedded in precast units or in in-situ structural elements or in both, but they should be effectively continuous. 6.1.2.4.3 Ties should be joined, generally using one of the methods described in 6.3.2, 6.3.3 or 6.3.4. 6.1.2.4.4 Ties connecting precast units should be so arranged as to minimize out-of-balance effects. 6.1.2.4.5 The minimum dimension of any in-situ concrete section in which tie bars are provided should be not less than the sum of the bar size (or twice the bar size at laps) plus twice the maximum aggregate size plus 10 mm. 6.1.2.4.6 The tie should be able to transmit the forces from the reinforcement in the precast units and to develop the required strength at all lapped joints. If enclosing links are used, the ultimate tensile resistance of the links should be not less than the ultimate tension in the tie. 6.1.2.4.7 Ensure that column and wall ties do not, for their anchorage at either end, rely solely on the bond of a straight plain bar. So bend or so hook plain bars as to provide the required anchorage in bearing on sound concrete unless they are welded or mechanically anchored to the main reinforcement in a precast unit. 6.1.2.4.8 As an alternative to providing the vertical ties recommended above for structures of five storeys or more, such structures may be designed in accordance with the provisions given below. 6.1.2.4.8.1 So design the structure that, at each storey in turn, if any single vertical load-bearing element (other than one complying with 6.1.2.4.8.2 becomes incapable of carrying its load, it does not cause the collapse of the structure or of any significant part thereof. In designing the structure for this condition, take into account any building components that are otherwise non-load-bearing. When reliance is placed on catenary action, make allowance for the horizontal reactions necessary for equilibrium. In the case of a wall, take the length under consideration to be a single load-bearing
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SABS 0100-1 Ed. 2.2 element such as the length between adjacent lateral supports or between a lateral support and a free edge. For the purposes of this definition of wall length only, a lateral support may be considered to occur at a) a stiffened section of the wall (not exceeding 1 m in length) capable of resisting a horizontal force of 1,5Ft kN per metre height of wall, or b) a substantial partition at right angles to the wall, provided that it is tied to the wall with a tie force equal to 0,5Ft kN per metre height of wall (a substantial partition may be taken as one having an average mass per unit area of at least 150 kg/m2), where Ft is a tie force as in 4.11.9.4. To comply with 6.1.2.4.8.2, ground floor columns that are exposed to the risk of impact by vehicles and that cannot be allowed to become ineffective, should be so designed as to withstand an appropriate impact. 6.1.2.4.8.2 Any vertical load-bearing element that cannot be allowed to become ineffective, together with its connections, shall be so designed as to withstand a load of 34 kN/m2 applied to it from any direction. Any horizontal element (or any part thereof) that provides lateral support vital to the stability of that vertical load-bearing element shall be so designed, together with its connections, as to withstand a load of 34 kN/m2 applied to it from any direction. Any element or lateral support so designed should also be capable of supporting the reaction from any attached building components also subject to a loading of 34 kN/m2 or such reaction as might reasonably be transmitted, having regard to the strength of the attached component and the strength of its connection. 6.1.2.4.9 In order to comply with 3.3.3.2, when a structure is designed in accordance with 6.1.2.2.8.1, or a vertical load-bearing element is designed in accordance with 6.1.2.2.8.2, take the partial safety factor for strength γm as 1,3 for concrete and 1,0 for steel. The partial safety factor for loads γf is 1,05. 6.1.2.4.10 Durability should be considered in the design and detailing of connections.
6.2 Precast concrete construction 6.2.1 Framed structures and continuous beams When the continuity of reinforcement or tendons through the connections or the interaction between units (or both) is such that the structure will behave as a frame or as a continuous beam, the analysis, redistribution of moments, and the design and detailing of individual units may all be in accordance with clause 4 or clause 5, as appropriate.
6.2.2 Slabs 6.2.2.1 Slabs consisting of wide precast units or of a series of narrow precast units with effective jointing between them capable of shear transfer, may be designed in accordance with 4.4 or 4.5 or 5.4, as appropriate. 6.2.2.2 When assessing the effect of concentrated loads (including partitions in the direction of span), ensure that the width of slab assumed to contribute to the support of the load does not exceed the width of the loaded area together with the width of three precast units and joints (when there is no topping) or the width of four precast units and joints (where the topping is at least 30 mm thick), unless test results substantiate the use of a wider area. In no case take the width as extending more than 0,25l on either side of the loaded area, where l is the span.
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SABS 0100-1 Ed. 2.2 6.2.3 Other precast units Design and detail other precast concrete units, including large panels, in accordance with the appropriate provisions of clause 4, clause 5 or subclause 6.5, and make provision for the appropriate connections as recommended in 6.3. Design precast units intended for use in composite constructions (see 6.4) as such, but also check or design for the conditions arising during handling, transportation and erection. In a floor or roof construction of hollow blocks supported by precast concrete ribs, pay particular attention to the bearing of blocks on the ribs when no topping is provided.
6.2.4 Bearings for precast units 6.2.4.1 Terms relating to bearings for precast units The following terms relate to bearings for precast units: a) simple bearing: a supported unit bears directly on a support, the effect of projecting steel or added concrete being discounted; b) dry bearing: a bearing with no intermediate padding material; c) bedded bearing: a bearing with contact surfaces that have an intermediate padding of cementitious material; d) non-isolated unit: a supported unit that, in the event of loss of an assumed support, would be capable of carrying its load by transverse distribution to adjacent units; e) bearing length: the length of support, supported unit or intermediate padding material (whichever is the least) measured along the line of support (see figure 27); and f) bearing width: the overlap of support and supported unit, measured at right angles to the line of support (see figure 27). 6.2.4.2 Concrete corbels 6.2.4.2.1 A corbel is a short cantilever beam in which the principal load is so applied that the distance av between the line of action of the load and the face of the supporting element is less than d (where d is the effective depth of the corbel at the face of the supporting element), and the depth at the outer end of the beam is at least one-half of the depth at the face of the supporting element. 6.2.4.2.2 Determine the depth at the face of the supporting element from shear conditions in accordance with 4.3.4.2 but limit av as specified above. 6.2.4.2.3 Design the main tension reinforcement in a corbel and check the strength of the corbel on the assumption that it behaves as a simple strut-and-tie system. Ensure that the reinforcement so obtained is at least 0,4 % of the section at the face of the supporting element and is adequately anchored. At the front face of the corbel, anchor the reinforcement either by welding to a transverse bar of equal strength or by bending the bars backwards to form a loop; in the latter case, ensure that the bearing area of the load does not project beyond the straight portion of the bars forming the main tension reinforcement. 6.2.4.2.4 When the corbel is designed to resist a stated horizontal force, provide additional reinforcement to transmit this force in its entirety; weld the reinforcement to the bearing plate and anchor it adequately within the supporting element.
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SABS 0100-1 Ed. 2.2 6.2.4.2.5 Provide shear reinforcement in the form of horizontal links distributed in the upper two-thirds of the effective depth of the corbel at the column face; ensure that this reinforcement is at least one-half of the area of the main tension reinforcement, and anchor it adequately. 6.2.4.2.6 Corbels should be designed for shrinkage and temperature stresses. 6.2.4.3 Continuous concrete nibs Where a continuous nib less than 300 mm deep provides a bearing, as on a boot lintel, design the nib as a short cantilever slab in accordance with the provisions given below: 6.2.4.3.1 Ensure that the projection of the nib is sufficient to provide an adequate bearing width for the type of unit to be supported (see 6.2.4.4). Give the reinforcement in the nib and any reinforcement in the supported unit a minimum nominal overlap in plan of 60 mm. 6.2.4.3.2 Assume the line of action of the design load to occur at the outer edge of the loaded area, i.e. at the front edge of the nib, or at the beginning of the chamfered edge, or at the outer edge of the bearing pad, as appropriate. 6.2.4.3.3 Take the maximum design bending moment as the distance from the line of action of the load to the nearest vertical leg of the links in the beam element from which the nib projects, times the load. (Ensure that the tension reinforcement in the nib is at least that required by 4.11.4, and anchor the reinforcement adequately.) 6.2.4.3.4 Extend the tension reinforcement (the area of the reinforcement being not more than that given in 4.11.5) as near to the front face of the nib as considerations of adequate cover will allow, and anchor it there, either by welding to a transverse bar of equal strength or by bending the bars through 180° to form loops in the horizontal or vertical plane (ensure that vertical loops are of a bar diameter not exceeding 12 mm). 6.2.4.3.5 Provide links in the element from which the nib projects. The links should be capable of transmitting (in addition to any other forces they resist) the load from the nib to the compression zone of the element. 6.2.4.4 Bearings for precast units 6.2.4.4.1 General Ensure that the bearing width (see 6.2.4.1(f)) of precast units is sufficient to provide a) a proper anchorage of the tension reinforcement (see 4.11.7), and b) a proper restraint against loss of bearing through movement. Do not use direct bearing connections as column/column or wall/wall connections, either with or without flexible padding. 6.2.4.4.2 Calculation of net bearing width For non-isolated units (see 6.2.4.1(d)), the net bearing width should be the greater of 40 mm and the value calculated from the equation: net bearing width =
design ultimate support reaction per unit (design effective bearing length x design ultimate bearing stress)
where the design effective bearing length is as in 6.2.4.4.3 and the design ultimate bearing stress is as in 6.2.4.4.4. For isolated units, the net bearing width should exceed that of non-isolated units (see 6.2.4.1(d)) by 20 mm.
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SABS 0100-1 Ed. 2.2 6.2.4.4.3 Design effective bearing length In the equation given in 6.2.4.4.2, the effective bearing length is the least of a) bearing length per element, b) one-half of bearing length per element plus 100 mm, and c) 600 mm. 6.2.4.4.4 Design ultimate bearing stress The design ultimate bearing stress is based on the weaker of the bearing surfaces and has the following value: a) for dry bearing on concrete: 0,4 fcu (an allowance for γm included); b) for bedded bearing on concrete: 0,6 fcu (an allowance for γm included); c) for the concrete face of a steel bearing plate cast into a unit or support and not exceeding 40 % of the bearing length: 0,8 fcu (an allowance for γm included). Bearings using flexible padding may be designed using stresses intermediate between those for dry and for bedded bearings. 6.2.4.5 Spalling at supports The outer edges of the concrete interface of precast units and the bearings are subject to spalling. Chamfers occurring within areas subject to spalling may be ignored when the outer edge of a supporting unit or the end of a supported unit is being determined (see figure 27). The recommendations for allowances for effects of spalling at supports and at the end edges of supported units are given below. 6.2.4.5.1 The distances to be assumed ineffective as bearing surfaces for the outer edges of supports in relation to the material of the support: a) steel: nil; b) concrete grade 30 or higher, plain or reinforced: 15 mm; c) brickwork or masonry: 25 mm; d) concrete of a grade lower than grade 30, plain or reinforced: 25 mm; e) reinforced concrete less than 300 mm deep at the outer edge: not less than the nominal cover to reinforcement on the outer face of the support; and f) reinforced concrete where vertical-loop reinforcement exceeds 12 mm diameter: nominal end cover plus inner radius of bend. Where unusual spalling characteristics are known to apply when particular constituent materials are being used, adjustment should be made to the distances recommended.
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SABS 0100-1 Ed. 2.2
Figure 27 — Schematic arrangement of allowance for bearing 6.2.4.5.2 The distances to be assumed ineffective as bearing surfaces for the end edges of supported units in relation to the reinforcement at bearing of the supported unit: a) straight bars, horizontal loops or vertical loops not exceeding 12 mm in diameter, close to end of element: the greater of 10 mm or cover; b) tendons or straight bars exposed at end of element: nil; and c) vertical-loop reinforcement of bar size exceeding 12 mm: nominal end cover plus inner radius of bend. 6.2.4.6 Allowance for construction inaccuracies The allowance for construction inaccuracies should cover deviations that can occur during the assembling of components, site construction, manufacture and erection, and may be assessed from a statistical analysis of measured or predicted deviation. Alternatively, for supported members of span up to 15 m and with average standards of accuracy, the allowance may be taken as the greatest of: a) 15 mm, or 3 mm per metre of distance between the faces of steel or precast concrete supports;
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SABS 0100-1 Ed. 2.2 b) 20 mm, or 4 mm per metre of distance between the faces of masonry supports; and c) 25 mm, or 5 mm per metre of distance between the faces of in-situ concrete supports. 6.2.4.7 Horizontal forces or rotation at a bearing The presence of horizontal forces at a bearing can reduce the load-carrying capacity of the supporting unit considerably by causing premature splitting or shearing. These forces may be due to creep, shrinkage, and temperature effects, or may result from misalignment, lack of plumb or other causes. When they are likely to be significant, consider these forces in designing and detailing the joints by providing a) either sliding bearings or suitable lateral reinforcement in the top of the supporting unit, and b) continuity reinforcement to tie together the ends of the supported units. Where, owing to large spans or other reasons, large rotations are likely to occur at the end supports of flexural units, use bearings that are capable of accommodating these rotations.
6.2.5 Joints between precast units 6.2.5.1 General 6.2.5.1.1 Design the critical sections of precast units close to joints to resist the worst combinations of shear, axial force and bending caused by the ultimate vertical and horizontal forces. When the design of the units is based on the assumption that the joint between them is not capable of transmitting moment, either design the joint to ensure that this is so (see 6.2.4.7) or take suitable precautions to ensure that if any cracking develops, it will not be unsightly and will not excessively reduce the unit's resistance to shear or axial force. 6.2.5.1.2 Where a space is left between two or more precast units, which is to be filled later with in-situ concrete or mortar, make the space large enough for the filling material to be placed easily and compacted sufficiently to fill the gap without abnormally high standards of workmanship or supervision. The assembly instructions shall specify clearly at what stage during construction the gap should be filled. As the majority of joints will incorporate a structural connection (see 6.3), give consideration to this aspect in the design of the joint. 6.2.5.2 Joints transmitting mainly compression 6.2.5.2.1 A joint that transmits mainly compression is most commonly used for horizontal joints between load-bearing walls or columns. Design the joint to resist all the forces and moments implicit in the assumptions made in analysing the structure as a whole and in designing the individual units to be joined. In the absence of more accurate information derived from a comprehensive programme of suitable tests, the area of concrete to be considered when the strength of the joint in a wall or column is being calculated, should be the greater of a) the area of the in-situ concrete, ignoring the area of any intruding floor or beam units (but not more than 90 % of the wall or column area), and b) 75 % of the area of contact between wall or column and joint. Consider only those parts of the floor units that are solid over the bearing, and bed the units properly on concrete or mortar of adequate quality.
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SABS 0100-1 Ed. 2.2 6.2.5.2.2 Pay particular attention to detailing the joint and joint reinforcement to prevent premature splitting or spalling of the concrete in the ends of the precast units. 6.2.5.2.3 Where a wall or a column is subjected to lateral loads, design the horizontal joints for shear in accordance with 6.5.3.14. 6.2.5.3 Joints transmitting shear in slabs A joint may be assumed to transmit a shear force between panels when, for example, a wall acts as a wind-bracing wall or a floor acts as a wind girder, provided that one of the provisions given below is complied with. 6.2.5.3.1 Floor units transmitting shear in a horizontal plane should be restrained to prevent their moving apart horizontally, and the joints between them should be formed by grouting with a suitable concrete or mortar mix. When the calculated shear stress in the joint under ultimate loads does not exceed 0,23 MPa, no reinforcement need be provided in or across the joint, and the sides of the unit forming the joint may have the normal finish. 6.2.5.3.2 When the sides or ends of the panels or units forming the joints have a finish "as-extruded" (see table 42), and when the shear stress due to ultimate loads does not exceed 0,45 MPa, no reinforcement need be provided in joints that are under compression in all loading conditions. 6.2.5.3.3 The shear stress due to design ultimate loads, calculated on the minimum root area of a castellated joint, should be less than 1,3 MPa. Separation of the units normal to the joint should be prevented either by the provision of steel ties across the ends of the joint or by the provision of a compressive force normal to the joint under all loading conditions. A taper should usually be provided to the projecting keys of a castellated joint to ease the removal of formwork; to limit movements in the joint, ensure that this taper is not excessive. 6.2.5.3.4 When reinforcement is provided to resist the entire shear force due to design ultimate loads, the shear force V should comply with the following equation: V = 0,6 Fb tan αf where Fb is the lesser of 0,87fyAs or the anchorage value of the reinforcement; As is the minimum area of reinforcement; fy is the characteristic strength of reinforcement; and αf is the angle of internal friction between faces of joint. Tan αf can vary between 0,7 and 1,7 and is best determined by tests. However, for concrete-to-concrete connections, the following values may be assumed: a) tan αf = 0,7 for a smooth interface, as in untreated concrete; b) tan αf = 1,4 for a roughened or castellated joint without continuous in-situ strips across the ends of joints; and c) tan αf = 1,7 for a roughened or castellated joint with continuous in-situ strips across the ends of joints.
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SABS 0100-1 Ed. 2.2 6.2.5.3.5 It should be able to be demonstrated that resistance to sliding of the joint is provided by other means; this would normally mean testing in accordance with 3.4.5. 6.2.5.4 Halving joint 6.2.5.4.1 For a halving joint, ensure that the maximum vertical ultimate load Fv does not exceed 4vcbdo, where b is the width of the beam, do is the effective depth of the half section and vc is the shear stress given in 4.3.4.1 for the full beam section. When determining the value of Fv, give consideration to the method of erection and the forces involved. 6.2.5.4.2 Detail reinforcement of the halving joint to suit the overall size and geometrical proportions of the joint. Several arrangements of reinforcement are possible and are covered in specialist literature. Inclined links may be used as the diagonal tension reinforcement where the line of action of Fv intersects the inclined link. If this is not the case, then use vertical and horizontal links. 6.2.5.4.3 The total force in the links may be determined by an appropriate truss analogy. The cross-sectional area of the links is then given by Fv
Asv =
0,87f yv cos 45E Fv
Asv =
0,87f yv
for links at 45E to the horizontal, and
for vertical and horizontal links,
where Asv
is the cross-sectional area of links; and
fyv
is the characteristic strength of links (but not more than 450 MPa).
6.2.5.4.4 Provide nominal vertical links in accordance with 4.11.4.5. So secure inclined links that they cannot be displaced. 6.2.5.4.5 Check the anchorage of all main reinforcement. In the tension face of the beam, transfer the horizontal component of force in inclined links Fh, which for 45E links is equal to Fv, to the main reinforcement. If the main reinforcement is straight without hooks or bends, the links may be considered anchored if Fh
2us lsb
< the anchorage bond stress given in table 24
where
Σu
is the perimeter of main reinforcement; and
lsb
is the length of straight reinforcement beyond intersection with link.
s
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SABS 0100-1 Ed. 2.2 6.2.5.4.6 If the main reinforcement is hooked or bent vertically, anchor the inclined links by bending them parallel to the main reinforcement; in this case, or if inclined links are replaced by bent-up bars, ensure that the bearing stress within the bends does not exceed the value given in 4.11.6.9. Bent-up bars may only be used to replace inclined links when effective end anchorage is possible (by means of welded cross-bars or other positive anchorage device). 6.2.5.4.7 Ensure that horizontal links are capable of carrying horizontal loads that may be applied to the joint in addition to the forces arising from the vertical reaction. 6.2.5.4.8 Place vertical links at the end of the full-depth section as near to the end face as possible.
6.3 Structural connections between units 6.3.1 General 6.3.1.1 Structural requirements for connections When designing and detailing the connections across joints between precast units, consider the overall stability of the structure, including its stability during construction or after accidental local damage. Take the provisions given in 6.1.2.4 into account and, in addition, consider the severe forces and stresses that may be applied to units during the various stages of handling, transportation and erection. Tie all units together adequately as soon as they have been placed in their final positions. When prestressed elements are built into supports, restrained creep effects should be considered. 6.3.1.2 Design method Design connections in accordance with the generally accepted methods applicable to reinforced concrete (see clause 4), prestressed concrete (see clause 5) or structural steel. Where, by the nature of the construction or material used, such methods are not applicable, prove the efficiency of the connection by appropriate tests in accordance with 3.4.5. 6.3.1.3 Considerations affecting design details In addition to ultimate strength requirements and the provisions given in 6.1.2.4 regarding minimum tying together of the structure, consider the provisions given below. 6.3.1.3.1 Protection So design connections that the standard of protection against weather, fire and corrosion that is required for the remainder of the structure is maintained. 6.3.1.3.2 Appearance Where connections are to be exposed, so design them that the quality of appearance required for the remainder of the structure can be readily achieved. This may often be better done by emphasizing the connections rather than by attempting to conceal them.
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SABS 0100-1 Ed. 2.2 6.3.1.3.3 Manufacture, assembly and erection During design, consider methods of manufacture, assembly and erection, and give particular attention to the following points: a) where projecting bars or sections are required, keep them to a minimum and make them as simple as possible; make such projections no longer than is necessary for security; b) avoid fragile fins and nibs; c) locate fixing devices of adequate strength in concrete sections; d) consider the practicability of both casting and assembly; e) most connections require the introduction of suitable jointing material; in the design, allow sufficient space for such material to ensure that the proper filling of the joint is practicable; f) it may be desirable to slacken, release or remove levelling devices such as nuts, wedges, etc., that have no load-bearing function in the completed structure; where this is necessary, ensure that the details are such that inspection (to make certain that this has been done) can be carried out without undue difficulty. 6.3.1.4 Site instructions 6.3.1.4.1 The strength and stiffness of any connection can be significantly affected by workmanship on site. The diversity of types of joints and their critical role in the strength and stability of the structure place a particular responsibility on the designer to make clear to those responsible for manufacture and erection, those details that are essential to the correct operation of the joint. 6.3.1.4.2 Consider the following points and, where necessary, pass specific instructions to the site: a) the sequence of forming the joint; b) critical dimensions, allowing for permitted deviations, e.g. minimum permissible bearing; c) critical details, e.g. accurate location of a particular reinforcing bar; d) the method of correcting possible lack of fit in the joint; e) details of temporary propping, and the stage at which it may be removed (see the relevant clause of SABS 0100-2); f) the description of the general stability of the structure, with details of any temporary bracing necessary; g) the extent to which the uncompleted structure may proceed above the completed and matured section; h) full details of special materials; and i) the weld sizes, fully specified (where weld symbols are used, ascertain that these are understood on site).
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SABS 0100-1 Ed. 2.2 6.3.2 Continuity of reinforcement 6.3.2.1 General requirements Where continuity of reinforcement is required through the connection, use a jointing method such that the assumptions made in analysing the structure and critical sections are realized. The following methods may be used to achieve continuity of reinforcement: a) lapping of bars; b) sleeving; c) threading of bars; d) welding; and e) any other method proven by tests in accordance with 3.4.5. 6.3.2.2 Lapping of bars Where straight bars passing through the joint are lapped, the provisions given in 4.11.6.6 apply. When reinforcement is grouted into a pocket or recess, provide an adequate shear key on the inside of the pocket. Where continuity over a support is achieved by having dowel bars pass through overlapping loops of reinforcement (which project from each supported element), make the bearing stresses inside the loops in accordance with 4.11.6.9. 6.3.2.3 Sleeving 6.3.2.3.1 Three principal types of sleeve jointing may be used, provided that the strength and deformation characteristics have been determined by tests in accordance with 3.4.5. The three types are a) grout-filled or resin-filled sleeves capable of transmitting both tensile and compressive forces; b) sleeves that mechanically align the square-sawn ends of two bars to allow the transmission of compressive forces only; and c) swaged connectors. 6.3.2.3.2 Ensure that the detailed design of the sleeve and the method of manufacture and assembly are such that the ends of the two bars will be accurately aligned into the sleeve. Ensure that the concrete cover provided for the sleeve is at least that specified for normal reinforcement. 6.3.2.4 Threading 6.3.2.4.1 The following methods may be used for jointing threaded bars: a) the threaded ends of bars may be joined by a coupler having left-hand and right-hand threads; this type of threaded connection requires a high degree of accuracy in manufacture in view of the difficulty of ensuring alignment;
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SABS 0100-1 Ed. 2.2 b) one set of bars may be welded to a steel plate, which is drilled to receive the threaded ends of the second set of bars; the second set of bars is fixed to the plate by means of nuts; and c) threaded anchors may be cast into a precast unit to receive the threaded ends of reinforcement. 6.3.2.4.2 When there is a risk of the threaded connection working loose, e.g. during vibration while in-situ concrete is being cast, use a locking device. 6.3.2.4.3 Restrict the threading of reinforcement to plain round mild steel bars. Where there is difficulty in producing a clean thread at the end of a bar, use steel that is normally specified for black bolts and that has a characteristic strength of 430 MPa. 6.3.2.4.4 Base the structural design of special threaded connections on tests in accordance with 3.4.5. Where tests have shown the threaded connection to be at least as strong as the parent bar, the strength of the joint may be based on 80 % of the specified characteristic strength of the joined bars in tension and on 100 % of that of bars in compression, divided in each case by the appropriate γm factor. 6.3.2.5 Welding of bars The design of welded connections may be in accordance with 4.11.6.7, provided that the welding is carried out as recommended in the relevant clause of SABS 0100-2.
6.3.3 Connections with structural steel inserts 6.3.3.1 Joints with structural steel inserts generally consist of a steel plate or rolled steel section projecting from the face of a column to support the end of a beam. Design the reinforcement in the ends of the supported beam in accordance with clause 4. 6.3.3.2 Design the steel sections and any bolted or welded connections in accordance with SABS 0162. Bearing stresses of up to 0,8fcu may be used, unless higher values can be justified by means of tests. 6.3.3.3 Except where the design ensures that the reaction does not act at the end of the steel section, base the design of the supported unit on a span equal to its overall length, including any projecting steel sections. For the design of the supporting unit and its projecting steel section, assume that the reaction is applied at the end of the projecting steel section. 6.3.3.4 In the design, consider the possibility of vertical splitting under the steel section due to shrinkage effects and localized bearing stresses, e.g. under a narrow steel plate.
6.3.4 Other types of connection Any other type of connection that can be shown to be capable of carrying the ultimate loads acting on it may be used. Amongst those suitable for resisting shear and flexure are those made by prestressing across the joint. Resin adhesives may be used to form joints subjected to compression but may not be used to resist tension or shear. Use them only where they are adequately protected from the effects of fire.
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SABS 0100-1 Ed. 2.2 6.4 Composite concrete construction 6.4.1 General 6.4.1.1 The provisions of this subclause apply to flexural composite elements consisting of precast concrete units acting in conjunction with added concrete where provision has been made for the transfer of horizontal shear at the contact surface. The precast units may be of either reinforced or prestressed concrete. Analyse and design composite concrete structures and elements in accordance with clause 4 or clause 5, modified, where appropriate, in accordance with 6.4.3 and 6.4.4. Pay particular attention, in the design of both the components and the composite section, to the effect of the method of construction, on stresses and deflections, and to whether or not propping is to be used. 6.4.1.2 Base the relative stiffnesses of elements on the properties of the concrete, gross or transformed sections, as described in 3.4.3.1. If the concrete strength in the two components of a composite element differs by more than 10 MPa, make allowance for this when stiffness is being assessed. 6.4.1.3 Differential shrinkage of the added concrete and precast concrete units may require consideration in analysing composite elements for the serviceability limit states (see 6.4.3.4); differential shrinkage need not be considered for the ultimate limit state. 6.4.1.4 When precast prestressed units, having pre-tensioned tendons, are designed as continuous elements and continuity is obtained with reinforced concrete cast in-situ over the supports, the compressive stresses due to prestress in the ends of the units may be ignored over the transmission length of the tendons when the strength of sections is being assessed.
6.4.2 Shear 6.4.2.1 Carry out the analysis of the resistance of composite sections to vertical shear due to design ultimate loads in accordance with 4.3.4 for reinforced concrete and 5.3.4 for prestressed concrete. However, when in-situ concrete is placed between precast prestressed units and the composite concrete section is used in design, ensure that the principal tensile stress does not exceed 0,24 f cu anywhere in the prestressed units; calculate this stress by making due allowance for the construction sequence and by taking into account only 0,8 of the compressive stress due to prestress at the section under consideration. 6.4.2.2 Calculations for horizontal shear between the two components of a composite section are governed by the ultimate limit state. The methods given in 6.4.4.1 to 6.4.4.4 ensure that composite action does not break down for the serviceability limit states and that the design shear strength is adequate for the ultimate limit state.
6.4.3 Serviceability limit states 6.4.3.1 General In addition to the provisions given in clause 4 and clause 5 concerning deflection and control of cracking, the design of composite construction will be affected by the provisions of the following subclauses. 6.4.3.2 Compression in the concrete in the case of prestressed precast units For composite elements comprising prestressed precast units and in-situ concrete, the methods of
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SABS 0100-1 Ed. 2.2 analysis may be as given in 5.3.3. However, the compressive stresses in the precast unit at the interface may be increased by not more than 50 % above the value given in table 29, provided that the ultimate failure of the composite element is due to excessive elongation of the steel. 6.4.3.3 Tension in the concrete in the case of prestressed precast units When there is a danger of corrosion (e.g. if there is non-prestressed reinforcement in the in-situ concrete), the flexural tensile stress in the in-situ concrete should be limited by crack control measures, in accordance with 4.3.7. Amdt 1, Apr. 1994
| | |
Table 41 - Deleted by amendment No. 1.
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Where continuity is obtained with reinforced concrete cast in-situ over the supports, the flexural tensile stresses and the hypothetical tensile stresses in the precast prestressed units at the supports should be limited in accordance with 5.3.2.3. Amdt 1, Apr. 1994
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6.4.3.4 Differential shrinkage 6.4.3.4.1 The effects of differential shrinkage are not generally of great importance in simply supported elements. However, where there is an appreciable difference between the age and quality of the concrete in the components, differential shrinkage may lead to increased stresses in the composite section and these must be investigated. The effects of differential shrinkage are likely to be more severe when the precast component is of reinforced concrete or of prestressed concrete with an approximately triangular distribution of stress due to prestress. In particular, the tensile stresses due to differential shrinkage may require consideration in design, and the engineer should refer to specialist literature in deciding when these stresses may be significant. 6.4.3.4.2 In the calculation of the tensile stresses, a value will be required for the differential shrinkage coefficient (the difference in total free strain between the two components of the composite element), the magnitude of which will depend on many variables. For a structure in a normal environment, and in the absence of more exact data, assume a value of 100 x 10-6 for the differential shrinkage when calculating stresses in composite T-beams with an in-situ concrete flange. 6.4.3.5 Continuity in composite construction 6.4.3.5.1 When continuity is obtained in composite construction by providing reinforcement over the supports, give consideration to the secondary effects of differential shrinkage and creep on the moments in continuous beams and on the reactions at the supports. Take the hogging restraint moment Mcs at an internal support of a continuous composite beam and slab section due to differential shrinkage as Mcs
= εdiffEcfAcfacent ψ
(19)
where εdiff
is the differential shrinkage strain;
Ecf
is the modulus of elasticity of the flange concrete;
Acf
is the area of effective concrete flange;
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SABS 0100-1 Ed. 2.2 acent is the distance from the centroid of the concrete flange to the centroid of the composite section;
ψ
is a reduction factor to allow for creep, taken as 0,37 (see 6.4.3.5.4).
6.4.3.5.2 The hogging restraint moment Mcs will be modified with time by creep due to self-weight load and creep due to any prestress in the precast units. The restraint moment due to prestress may be taken as the restraint moment that would have been set up if the composite section as a whole had been prestressed, multiplied by a reduction factor ψ1 taken as 0,92 (see also 6.4.3.5.4). 6.4.3.5.3 Use the information given in 6.4.3.4 for assessing a value for the differential shrinkage strain. 6.4.3.5.4 Equation (19) for calculating the restraint moments due to creep and differential shrinkage is based on an assumed value of 2,5 for the ratio βcc of total creep to elastic deformation. If the design conditions are such that this value is significantly low, then the engineer should calculate values for the reduction factors ψ and ψ1 from the following:
ψ ψ1
(1 e
βcc
)
βcc
(1 e
βcc
)
where e is the base of Napierian logarithms.
6.4.4 Ultimate limit state 6.4.4.1 Horizontal shear force due to design ultimate loads The interface of the precast and in-situ components occurs either in the tension zone or in the compression zone affecting the horizontal shear force due to design ultimate loads so that this shear force is either: a) where the interface is in the compression zone: the compression from that part of the compression zone above the interface, calculated from the ultimate bending moment; or b) where the interface is in the tension zone: the total compression (or tension) calculated from the ultimate bending moment. 6.4.4.2 Average horizontal design shear stress The average horizontal design shear stress is calculated by dividing the design horizontal shear force (see 6.4.4.1) by the area obtained by multiplying the contact width by the beam length between the point of maximum positive or negative design moment and the point of zero moment.
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The average horizontal design shear stress should then be distributed in proportion to the vertical design shear force diagram, to give the horizontal shear stress at any point along the length of the composite component. The horizontal design shear stress v so detained, should nowhere exceed the Amdt 2, Mar. 2000 appropriate value in table 42.
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SABS 0100-1 Ed. 2.2 Table 42 - Design ultimate horizontal shear stresses at interface
Design ultimate horizontal shear stresses at interface Precast unit
I
Surface type
I
Grade of in-situ concrete MPa 25
Without links
As-cast or as-extruded
1
0,4
/ With nominal links projecting into in-situ concrete
Washed to remove laitance or treated with retarder and cleaned
1
0,6
I
2
40
I
0,55
I
I
Brushed, screeded or rough-tamped
30 I
1
0,65
I 0,65
I
0,75
I
0,7
0,75
0,80
As-cast or as-extruded
1,2
1,8
2,o
Brushed, screeded or rough-tamped
1,8
2,O
22
Washed to remove laitance or treated with retarder and cleaned
21
2.2
2.3
NOTES
1 The description "as-cast" covers those cases where the concrete is placed and vibrated, leaving a rough finish. The surface is rougher than would be required for finishes to be applied directly without a further finishing screed but not as rough as would be obtained if tamping, brushing or other artificial roughening had taken place. 2 The description "as-extruded" covers those cases in which an open-textured surface is produced direct from an extruding machine. 3 The description "brushed, screeded or rough-tamped" covers those cases where some form of deliberate surface roughening has taken place but not to the extent of exposing the aggregate. 4 For structural assessment purposes, it may be assumed that the appropriate value of v, (included in the table) is 1 3 .
6.4.4.3 Nominal links Where nominal links are provided, they should be of cross-section at least 0,15 % of the contact area. Spacing should not be excessive. The spacing of links in T-beam ribs with composite flanges should not exceed the greater of four times the minimum thickness of the in-situ concrete or 600 mm. Links should be adequately anchored on both sides of the interface. 6.4.4.4 Links in excess of minimum Where the horizontal shear stress from 6.4.4.2 exceeds the value given in table 42, all the horizontal shear force should be carried on reinforcement anchored on either side of the interface. The amount of steel required, A, (in square millimetres per metre) should be calculated from the following equation:
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SABS 0100-1 Ed. 2.2 Ah =
1 000 bvh 0,87f y
where b
is the contact width;
vh is the average horizontal design shear stress, as in 6.4.4.2; and fy
is the characteristic strength of links.
6.4.4.5 Differential shrinkage between added concrete and precast units Differential shrinkage between added concrete and precast units need not be considered for the ultimate limit state.
6.4.5 Thickness of structural topping The recommended minimum thickness of structural topping is 40 mm nominal with a local minimum of 25 mm.
6.5 Plain concrete walls 6.5.1 General 6.5.1.1 A plain concrete wall is a vertical load-bearing concrete element whose greatest lateral dimension exceeds four times its least lateral dimension, and one that is assumed to be without reinforcement when its strength is being considered. 6.5.1.2 Where the greatest lateral dimension is less than four times the thickness, the provisions of this clause may still be applied. 6.5.1.3 The definitions for short, slender, braced or unbraced reinforced concrete walls given in 4.8.1 also apply to a plain concrete wall.
6.5.2 Structural stability The subclauses related to reinforced concrete walls may be applied (see 4.8.2).
6.5.3 Design of plain concrete walls 6.5.3.1 Axial force The design ultimate axial force in a plain concrete wall may be calculated on the assumption that the beams and slabs transmitting forces into it are simply supported. 6.5.3.2 Effective height of unbraced plain concrete walls The effective height l e of an unbraced plain concrete wall should be taken as follows: a) in the case of a wall supporting at its top a roof or floor slab spanning at right angles: le = 1,5 lo b) in the case of other walls: le = 2 lo
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SABS 0100-1 Ed. 2.2 where lo is the clear height of the wall between lateral supports; for gable walls, lo may be measured midway between eaves and ridge. 6.5.3.3 Effective height of braced plain concrete walls The effective height of braced plain concrete walls should be taken as follows: a) where the lateral supports provide resistance both to lateral movement and to rotation, le equals three-quarters of the clear distance between lateral supports or twice the distance between a support and a free edge, as appropriate; NOTE - This distance is measured vertically if the lateral supports are horizontal (e.g. floors) or horizontally if the lateral supports are vertical (e.g. other walls).
b) where the lateral supports provide resistance to lateral movement only, le equals the distance between centres of supports, or two and a half times the distance between a support and a free edge, as appropriate. 6.5.3.4 Limits of slenderness The slenderness ratio le/h should not exceed 30, whether the wall be braced or unbraced. 6.5.3.5 Minimum transverse eccentricity of forces Whatever the arrangements of vertical or horizontal forces, the resultant force in every plain concrete wall should be assumed to have a transverse eccentricity of the greater of at least h/20 or 20 mm. In the case of a slender wall, additional eccentricity can arise as a result of deflection under load. Procedures allowing for this are given in 6.5.3.12 and 6.5.3.13. 6.5.3.6 Eccentricity in the plane of the wall 6.5.3.6.1 In the case of a single wall in-plane Eccentricity due to forces may be calculated by statics alone. 6.5.3.6.2 In a case where a horizontal force is resisted by two or more parallel walls The force should be assumed to be shared between the walls in proportion to their relative stiffnesses, provided the resultant eccentricity in any individual wall does not exceed one-third of the length of that wall. Where the eccentricity in any individual wall is found to exceed this, the wall stiffness should be regarded as zero and an adjustment made to the forces that are assumed to be carried by the remaining wall(s). 6.5.3.6.3 In the case of a shear connection being assumed between vertical edges of adjacent walls An appropriate elastic analysis may be made, provided the shear connection is designed to resist the design ultimate forces. 6.5.3.7 Eccentricity at right angles to the wall 6.5.3.7.1 The load transmitted to a wall by a concrete floor or roof may be assumed to act at one-third of the depth of the bearing area from the loaded face. Where there is an in-situ concrete floor on either side of the wall, the common bearing area may be assumed to be shared equally by each floor.
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SABS 0100-1 Ed. 2.2 6.5.3.7.2 Loads may be applied to walls at eccentricities exceeding half the thickness of the wall by means of special fittings (e.g. joist hangers), provided that the adequacy of such fittings against local failure is proved by testing or other means. 6.5.3.7.3 The resultant eccentricity of the total load on a braced wall at any level may be calculated on the assumption that, immediately above a lateral support, the resultant eccentricity of all the vertical loads above that level is zero. 6.5.3.8 In-plane and transverse eccentricity of resultant force on an unbraced wall At any level, full allowance should be made for the eccentricity of all vertical loads and the overturning moments produced by any lateral forces above that level. 6.5.3.9 Concentrated loads When loads are purely local (as at beam bearings), they may be assumed to be immediately dispersed, provided that the local design stress under the load does not exceed 0,6fcu for concrete of grade 25 or higher, or 0,5fcu for concrete of a lower grade. 6.5.3.10 Calculation of design load per unit length The design load per unit length nw should be assessed on the basis of a linear distribution of load along the length of the wall, with no allowance for any tensile strength. 6.5.3.11 Maximum unit axial load for short braced plain walls The maximum design ultimate axial load per unit length of wall due to ultimate loads, nw, should satisfy the following equation: nw < 0,3 (h - 2ex) fcu
(20)
where nw is the maximum design axial load per unit length of wall due to design ultimate loads; h
is the thickness of wall;
ex is the resultant eccentricity of load at right angles to plane of wall (see 6.5.3.5 for minimum value); and fcu is the characteristic strength of concrete. 6.5.3.12 Maximum unit axial load for slender braced plain walls At every section of a slender braced wall, the maximum design axial load nw should satisfy equation (20) and, additionally, the following: nw < 0,3 (h - 1,2ex - 2ea) fcu
(21)
where nw, h, ex and fcu are as in 6.5.3.11; and ea is the additional eccentricity due to deflections, which may be taken as le2/2 500 where le is the effective height of the wall.
160
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SABS 0100-1 Ed. 2.2 6.5.3.13 Maximum unit axial load for unbraced plain walls The maximum unit axial load at every section of an unbraced plain wall should satisfy the following two conditions: a) nw < 0,3 (h - 2ex1) fcu b) nw < 0,3 [h - 2(ex2 + ea)] fcu where nw, h, ea, and fcu are as in 6.5.3.11 and 6.5.3.12; ex1 is the resultant eccentricity calculated at top of wall (see 6.5.3.7); and ex2 is the resultant eccentricity calculated at bottom of wall (see 6.5.3.7). 6.5.3.14 Shear strength The design shear resistance of plain walls need not be checked if one of the following conditions is satisfied: a) the horizontal design shear force is less than one-quarter of the design vertical load; or b) the horizontal design shear force is less than that required to produce an average design shear stress of 0,45 MPa over the whole wall cross-section. NOTE - For concrete of grades lower than grade 25 and for lightweight aggregate concrete, the figure of 0,30 MPa should be used instead of 0,45 MPa.
6.5.3.15 Cracking of concrete Reinforcement may be needed in walls to control cracking due to flexure or thermal and hydration shrinkage (see 6.5.3.16 to 6.5.3.18). Wherever reinforcement is provided, the quantity should be: a) for reinforcement of grade 450: at least 0,25 % of the concrete cross-sectional area; and b) for reinforcement of grade 250: at least 0,30 % of the concrete cross-sectional area. 6.5.3.16 Reinforcement in plain walls for flexure If, at any level, a length of wall exceeding one-tenth of the total length is subjected to tensile stress resulting from in-plane eccentricity of the resultant force, vertical reinforcement may be necessary to distribute potential cracking. Reinforcement need only be provided in the area of wall found to be in tension under design service loads. It should be arranged in two layers and should comply with the spacing rules given in 4.11.8.2. 6.5.3.17 Reinforcement in plain walls to counteract cracks resulting from shrinkage and temperature 6.5.3.17.1 Plain concrete walls that exceed 2 m in length and are cast in-situ, may have to be reinforced to control cracking arising from shrinkage and temperature effects, including temperature rises caused by the heat of hydration released by the cement. Reinforcement for this purpose should be considered as follows: a) in an external plain wall directly exposed to the weather, reinforcement should be provided in both
161
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SABS 0100-1 Ed. 2.2 horizontal and vertical directions; it should consist of bars of small diameter, relatively closely spaced, with adequate cover near the exposed surface (see also 6.5.3.15); b) in an internal wall it may only be necessary to provide reinforcement in that part of the wall where junctions with floors and beams occur, in which case it should be equally dispersed between each face (see also 6.5.3.15). 6.5.3.17.2 In general, it will not be necessary to provide reinforcement to counteract shrinkage and temperature effects in walls made of no-fines concrete. 6.5.3.18 Reinforcement around openings in plain walls Nominal reinforcement should be considered. 6.5.3.19 Deflection of plain concrete walls The deflection in a plain concrete wall will be within acceptable limits if the preceding provisions have been conformed to and if, in the case of a cantilever shear wall, the total height of the wall does not exceed ten times its length.
7 Fire resistance 7.1 General 7.1.1 When a structural concrete element is subjected to fire, it undergoes a gradual reduction in strength and rigidity. For limit state design, therefore (as stated in 3.2.4.3), there are three conditions to be considered: a) retention of structural strength; b) resistance to penetration of flames; and c) resistance to heat transmission. The first criterion is applicable to all structural elements while the other two criteria are applicable to walls and floors, which perform a separating function.
7.1.2 The requirements for fire resistance for various elements in a structure are either checked by a standard test on a specimen or satisfied by suitable choices based on the data given in this clause. NOTE - Standard fire tests are not intended to give information on the use of an element after it has been subjected to fire.
7.1.3 The following factors influence the fire resistance of concrete structures (some of these factors cannot be taken into account quantitatively): a) the size and shape of the element; b) the type of concrete; c) the type of reinforcement or tendon; d) the protective concrete cover provided to reinforcement or tendons (see 7.1.9);
162
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 e) the load supported; and f) the conditions of restraint.
7.1.4 Concretes made with siliceous aggregates have a tendency to spall when exposed to high temperatures but this tendency can be reduced by the incorporation of supplementary reinforcement in the concrete cover. Spalling does not generally occur with either calcareous or lightweight aggregates. The insulation properties of concrete made from lightweight aggregates are superior to those of concrete made from siliceous and calcareous aggregates. Other measures that may be taken to prevent spalling from occurring are a) a finish of plaster, vermiculite, etc., applied by hand or sprayed; b) the provision of a false ceiling as a fire barrier; and c) the use of sacrificial tensile steel.
7.1.5 Concrete, prestressing tendons, and reinforcement show a reduction in strength at high temperatures. At about 400 °C, tendons are likely to lose about 50 % of their strength at ambient temperature and in the case of reinforcement, a similar reduction in strength occurs at about 550 °C.
7.1.6 The fire resistance of structural elements is generally determined when the element is supporting its service load, which is taken as the sum of all the nominal self-weight and imposed loads. Tables 43 to 46 show the minimum dimensions for various elements when these loads are to be supported; any reduction in load will be reflected by an increase in fire resistance, but there are not sufficient data available to define the relationship. 7.1.7 Recent investigations have shown that the provision of end restraint against thermal expansion can substantially increase the fire resistance of a structural element. Until this aspect is more fully investigated, it is proposed that in beams and slabs so built into a structure that restraint against thermal expansion caused by fire would be provided at two opposite ends, the amount of protective cover to reinforcement and tendons be reduced to the value shown for the next lower period in tables 43 to 46. Thermal restraint can be assumed to be provided by the surrounding structure if no gaps or combustible materials exist between the structure and the ends of the floor or beam and if the surrounding structure is capable of withstanding the thermal stresses induced by the heated floor or beam.
7.1.8 In tables 43 to 50 (inclusive), the "minimum dimension" and the "minimum thickness" quoted are all recommended dimensions that are subject to the dimensional deviations given in SABS 0100-2. 7.1.9 Where plaster or sprayed fibre is used as an applied finish to elements other than the ones in tables 43 to 50, it may be assumed that the thermal insulation provided is at least equivalent to the same thickness of concrete. Such finishes can therefore be used to remedy deficiencies in cover thickness. For selected materials, the following guidance can be given with respect to allowing the use of additional protection not exceeding 25 mm in thickness as a means of providing effective cover to steel reinforcing or prestressing elements. In each case, the equivalent thickness of concrete may be replaced by the protection named. Mortar Gypsum plaster
0,6 x concrete thickness
Lightweight plaster
1,0 x concrete thickness; < 2 h
Sprayed lightweight insulation
2,0 x concrete thickness; > 2 h
163
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SABS 0100-1 Ed. 2.2 Vermiculite slabs
1,0 x concrete thickness; < 2 h 1,5 x concrete thickness; > 2 h
(See also table 47 for the effect of soffit treatment on the fire resistance of slabs.)
7.2 Beams 7.2.1 The fire resistance of a reinforced or prestressed concrete beam depends on the amount of protective cover, consisting of concrete with or without an insulating encasement, provided to the reinforcement or tendons. It is also necessary that the beam have a minimum width to avoid failure of the concrete before the reinforcement or tendons reach the critical temperature. For I-beams, the web thickness bw of a fully exposed beam should be at least 0,5 of the minimum width stated in tables 43 and 44 for the fire resistance of various beams. 7.2.2 Typical performances are given in table 43 for reinforced concrete beams and in table 44 for prestressed concrete beams, both for siliceous aggregate concrete and for low-density aggregate concrete.
7.2.3 The average concrete cover is determined by summing the product of the cross-sectional area of each bar or tendon and the distance from the surface of the bar to the nearest relevant exposed face, and dividing the sum by the total area of these bars or tendons. Only those bars or tendons provided for the purpose of resisting tension due to ultimate loads should be considered in this calculation. When reinforcement is used in combination with tendons, its total area should be used. 7.2.4 Tables 43 and 44 give the average concrete cover required to provide the stated fire resistance, but in no case may the nominal concrete cover to any bar or tendon be less than half this value, or less than the value given for the half-hour period appropriate to that form of construction.
7.2.5 In addition, in certain cases where siliceous aggregate concrete is used, it will be necessary to consider the provision of supplementary reinforcement to hold the concrete cover in position.
7.2.6 Supplementary reinforcement will be required in those cases indicated in tables 43 and 44 where the cover to all the bars and tendons under consideration exceeds 40 mm. When used, supplementary reinforcement shall consist of expanded metal lath or a wire fabric not lighter than 0,5 kg/m2 (2 mm diameter wires at centres not exceeding 100 mm) or a continuous arrangement of links at centres not exceeding 200 mm, incorporated in the concrete cover at a distance not exceeding 20 mm from the face.
164
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SABS 0100-1 Ed. 2.2 Table 43 - Fire resistance of reinforced concrete beams 1
2
3
4
5
6
7
Minimum dimension of concrete mm Description
Fire resistance h 4
3
2
1,5
1
0,5
a) Siliceous aggregate concrete: 1) average concrete cover to main reinforcement . . . . . . . . . . . . . . . . . . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*)65 280
*)55 240
*)45 180
35 140
25 110
15 80
b) As in (a) with cement or gypsum, 15 mm thick, with light mesh reinforcement: 1) average concrete cover to main reinforcement . . . . . . . . . . . . . . . . . . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*)50 250
40 210
30 150
20 110
15 85
15 70
c) As in (a) with vermiculite/gypsum plaster**) or sprayed asbestos, 15 mm thick, on light mesh reinforcement securely fixed to the beam: 1) average concrete cover to main reinforcement . . . . . . . . . . . . . . . . . . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*)25 170
15 145
15 115
15 85
15 60
15 60
d) Low density aggregate concrete: 1) average concrete cover to main reinforcement . . . . . . . . . . . . . . . . . . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
50 250
45 200
35 160
30 130
20 100
15 80
*)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.2.6). **)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
7.2.7 For I-beams, the average concrete cover determined as in 7.2.3 is adjusted by multiplying it by 0,6 to allow for the additional heat transfer through the upper flange face.
165
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SABS 0100-1 Ed. 2.2 Table 44 - Fire resistance of prestressed concrete beams
|
Amdt 1, Apr. 1994 1
2
3
4
5
6
7
Minimum dimension of concrete mm Description
Fire resistance h 4
3
2
1,5
1
0,5
a) Siliceous aggregate concrete: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*)100 280
*)85 240
*)65 180
*)50 140
40 110
25 80
b) As in (a) with vermiculite concrete slabs, 15 mm thick, used as permanent shuttering: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 75 210
*)60 170
*)45 125
35 100
25 70
15 70
c) As in (b) but with slabs 25 mm thick: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
65 180
50 140
35 100
25 70
15 60
15 60
d) As in (a) with gypsum plaster, 15 mm thick, with light mesh reinforcement 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 90 250
*)75 210
*)50 150
40 110
30 85
15 70
e) As in (a) with vermiculite/gypsum plaster**) or sprayed asbestos, 15 mm thick: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 75 170
*)60 145
*)45 115
30 85
25 60
15 60
f) As in (e) but with coating 25 mm thick: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 50 140
*)45 125
30 100
25 70
15 60
15 60
g) Low-density aggregate concrete: 1) average concrete cover to tendons . . . . 2) beam width . . . . . . . . . . . . . . . . . . . . . .
80 250
65 200
50 160
40 130
30 100
20 80
*)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.2.6). **)Vermiculite/gypsum plaster must have a mix ratio in the range 1,5:1 to 2:1 by volume.
166
5
6
25 100 175
**)55 **)55 140 150 **)55 **)30 70 150 **)55 **)30 60 150
25 125 190
**)65 **)65 150 150 **)65 **)40 75 150 **)65 **)40 70 150
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . . Width of rib, or beam, at soffit . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to reinforcement . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . Least width of downstanding leg . . . . . . . . . . . . . . . . . . . . Thickness of flange*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average bottom cover to reinforcement . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . Least width of each downstanding leg . . . . . . . . . . . . . . . . Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average bottom cover to reinforcement . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . Least width of each downstanding leg . . . . . . . . . . . . . . . . Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
d) Ribbed floors having hollow infill blocks of clay, or inverted Tsection beams with hollow infill blocks of concrete or clay. A floor in which less than 50 % of the gross cross-section is solid material shall be provided with a 15 mm plaster coating on soffit
e) Upright T-sections
Inverted channel sections with radius at intersection of soffits with top of leg not exceeding depth of section
f)
g) Inverted channel sections or U-sections with radius at intersection of soffits with top of leg exceeding depth of section
25 40 205 25 50 230
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . . Thickness of bottom flange . . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c) Hollow box sections having one or more longitudinal cavities, which are wider than they are high
**)45 **)25 50 100
**)45 **)25 60 125
**)45 **)45 115 125
20 90 160
20 40 180
35 20 40 100
35 20 50 125
35 35 90 125
20 80 140
20 30 155
25 15 35 75
25 15 40 100
25 25 75 100
15 70 110
15 25 130
15 10 25 65
15 10 30 90
15 15 60 90
15 50 100
15 20 105
15 20 100 15 25 110 20 30 140 20 40 160 25 40 175
25 50 190
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . . Thickness under cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b) Cored slabs in which the cores are circular or are higher than they are wide. Not less than 50 % of the gross cross-section of the floor should be solid material
15 100
0,5 15 100
1 20 125
1,5 20 125
2
h
Fire resistance
mm
7
25 150
3
25 150
*)Non-combustible screeds and floor finishes may be included in these dimensions. **)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.3).
4
Minimum dimension of concrete
3
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2
a) Solid slab
Floor construction
1
Table 45 - Fire resistance of reinforced concrete floors (silliceous or calcareous aggregate) This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
167
168 5
6
50 100 175
**)85 **)85 200 150 **)85 **)45 100 150 **)85 **)45 90 150
65 125 190
**)100 **)100 250 150 **)100 **)50 125 150 **)100 **)50 110 150
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . . Width of rib, or beam, at soffit . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . Least width of downstanding leg . . . . . . . . . . . . . . . . . . . . . Thickness of flange*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . Least width of each downstanding leg . . . . . . . . . . . . . . . . . Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . . Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . Least width of each downstanding leg . . . . . . . . . . . . . . . . . Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
d) Ribbed floors having hollow infill blocks of clay, or inverted Tsection beams with hollow infill blocks of concrete or clay. A floor in which less than 50 % of the gross cross-section is solid material shall be provided with a 15 mm plaster coating on soffit
e) Upright T-sections
f) Inverted channel sections with radius at intersection of soffits with top of leg not exceeding depth of section
g) Inverted channel sections or U-sections with radius at intersection of soffits with top of leg exceeding depth of section
50 50 205 65 50 190
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . . Thickness of bottom flange . . . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c) Hollow box sections having one or more longitudinal cavities, which are wider than they are high
**)65 **)35 70 125
**)65 **)35 75 125
**)65 **)65 150 125
40 90 160
40 40 180
50 25 55 125
50 25 60 125
50 50 120 125
30 80 140
30 30 155
40 20 45 100
40 20 45 100
40 40 90 100
25 70 110
25 25 130
25 15 30 90
25 15 30 90
25 25 60 90
15 50 100
15 20 105
15 20 100 25 25 110 30 30 140 40 40 160 50 40 175
65 50 190
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . . Thickness under cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b) Cored slabs in which the cores are circular or are higher than they are wide. Not less than 50 % of the gross cross-section of the floor should be solid material
15 90
25 100
0,5 30 125
1
40 125
1,5
50 150
65 150
2
h
Fire resistance
mm
7
3
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . . Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
*)Non-combustible screeds and floor finishes may be included in these dimensions. **)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.3).
4
Minimum dimension of concrete
3
4
2
a) Solid slab
Floor construction
1
Table 46 - Fire resistance of prestressed concrete floors (siliceous or calcareous aggregate)
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2
This standard may only be used by approved subscription and freemailing clients of the SABS.
SABS 0100-1 Ed. 2.2 7.3 Floors 7.3.1 The fire resistance of a floor depends on the minimum thickness of the concrete section and the average concrete cover to the reinforcement in the tensile zone. The performance of some typical reinforced concrete floors is given in table 45 and the performance of some typical prestressed concrete floors is given in table 46. The performance of floors of shapes not given may be assessed by analogy.
7.3.2 Non-combustible screeds or floor finishes may be taken into account in the estimation of the thickness of concrete. 7.3.3 The average concrete cover is determined by summing the product of the cross-sectional area of each bar or tendon and the distance from the surface of the bar to the nearest relevant exposed face, and dividing the sum by the total area of these bars or tendons. Only those bars or tendons provided for the purpose of resisting tension due to ultimate loads should be considered in this calculation.
7.3.4 Tables 45 and 46 give the average concrete cover required to provide the stated fire resistance, but in no case may the nominal concrete cover to any bar or tendon be less than half this value, or less than the value given for the half-hour period appropriate to that form of construction. 7.3.5 In addition, in certain cases where siliceous aggregate concrete is used, it will be necessary to consider the provision of supplementary reinforcement to hold the concrete cover in position.
7.3.6 Supplementary reinforcement will be required in those cases indicated in table 47 where no ceiling protection is provided (see 7.4) and the cover to all the bars and tendons under consideration exceeds 40 mm. When used, supplementary reinforcement shall consist of expanded metal lath or a wire fabric not lighter than 0,5 kg/m 2 (2 mm diameter wires at centres not exceeding 100 mm) or a continuous arrangement of links at centres not exceeding 200 mm, incorporated in the concrete cover Amdt 1, Apr. 1994 at a distance not exceeding 20 mm from the face.
7.3.7 In the absence of adequate test data, low-density concrete floors should be treated as dense concrete floors even though the fire resistance of the former might be expected to be somewhat superior.
7.3.8 In the case of hollow slabs (or beams with filler blocks), the effective thickness d should be obtained by considering the total solid material per unit width te as follows: t e h ξ t f where h
is the actual thickness of slab;
ξ
is the proportion of solid material per unit width of slab; and
tf
is the thickness of non-combustible finish.
7.4 Additional protection to floors The fire resistance of any given form of floor construction may be improved by the provision of an insulating finish on the soffit or by a suitable suspended ceiling, some examples of which are given in table 47.
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SABS 0100-1 Ed. 2.2 Table 47 - Effect of soffit treatment 1
2
3
4
Minimum thickness of finish mm Ceiling finish
Increase in fire resistance h
a)
b)
c)
Vermiculite/gypsum plaster*) or sprayed asbestos with light mesh reinforcement fixed securely to the underside of the slab (as in table 45) . . . . . . . . . . . . . . . . . . . . . . Vermiculite/gypsum plaster*) or sprayed asbestos**) on expanded metal as a suspended ceiling to floor construction 5-7 (as in table 45) . . . . . . . . . . . . . . . . . . . . . . Gypsum/sand or cement/sand on expanded metal as a suspended ceiling to any floor type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1,5
1
0,5
15
10
10
10
10
10
15
10
10
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume. **)When suspended ceilings are used, the increased fire resistance only holds if ducts, light fittings, etc., do not penetrate the ceiling and if services and combustible materials are kept out of the space between the ceiling and the floor construction above.
7.5 Columns 7.5.1 The minimum dimension of a column is a determining factor in the fire resistance it can provide. The dimensions given in table 48 relate to columns that, when subjected to service loads, may be exposed to fire on all faces. The use of limestone or other calcareous aggregates will, as indicated, reduce spalling and allow a reduction in the size of the section. When siliceous aggregates are used, the concrete cover to the main bars should not exceed 40 mm unless supplementary reinforcement is provided. Ensure that the cover to reinforced concrete columns is the same as that given in table 43 for beams.
7.5.2 Supplementary reinforcement shall consist of either a wire fabric not lighter than 0,5 kg/m2 (2 mm diameter wires at centres not exceeding 100 mm) or a continuous arrangement of links at centres not exceeding 200 mm, incorporated in the concrete cover at a distance not exceeding 20 mm from the face.
7.5.3 When supplementary reinforcement as in item (b) of table 48 is used to obtain a reduced size of column, it should be placed at mid-cover but not more than 20 mm from the face, and should be in the shape of a rectangular or circular cage.
7.5.4 Columns that are built into fire-resistant walls to their full height are likely to be exposed to fire on one face only. Where fire-resistant walls are required to have the same fire-resistance rating as the columns, the data given in table 49 apply to the situation where the face of the column is flush with the
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SABS 0100-1 Ed. 2.2 wall or where that part embedded in the wall is structurally adequate to support the load, provided that any opening in the wall is not nearer to the column than the minimum dimension specified in table 49 for that column. Table 48 - Fire resistance of concrete columns (all faces exposed) 1
2
3
4
5
6
7
Minimum dimension of concrete mm Type of construction
Fire resistance h
a) Siliceous aggregate concrete: 1) without additional protection . . . . . . . . . . . . 2) with cement or gypsum plaster, 15 mm thick, on light mesh reinforcement . . . . . . . . 3) with vermiculite/gypsum plaster*) or sprayed asbestos, 15 mm thick, on light mesh reinforcement securely fixed to the column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b) Limestone aggregate concrete or siliceous aggregate concrete, with supplementary reinforcement in concrete cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c) Low-density aggregate concrete . . . . . . . . . .
4
3
2
1,5
1
0,5
450
400
300
250
200
150
300
275
225
150
150
150
275
225
200
150
120
120
300
275
225
200
190
150
300
275
225
200
150
150
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
Table 49 - Fire resistance of concrete columns (one face exposed) 1
2
3
4
5
6
7
Minimum dimension of concrete mm Fire resistance
Type of construction
h
a) Siliceous aggregate concrete: 1) without additional protection . . . . . . . 2) with vermiculite/gypsum plaster*) or sprayed asbestos, 15 mm thick, on exposed faces on light mesh reinforcement securely fixed to the column . . . . . . . . . . . . . . . . . . . . . . . .
4
3
2
1,5
1
0,5
300
250
200
150
100
100
200
150
120
100
90
90
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
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SABS 0100-1 Ed. 2.2 7.6 Walls 7.6.1 Concrete walls containing at least 1,0 % of vertical reinforcement The fire resistance of concrete walls containing at least 1,0 % of vertical reinforcement is given in table 50. The minimum thicknesses shown are for siliceous aggregate concrete. When low-density aggregate concrete is used, a reduction in thickness is permissible if the fire resistance of such a wall is confirmed by a test. Concrete cover to the reinforcement should be at least 15 mm for a fire resistance of up to 1 h, and at least 25 mm for a fire resistance for longer periods. Unless shown otherwise by a test, walls containing vertical reinforcement of less than 1,0 % are regarded as plain concrete walls (see 7.6.2) for fire-resistance purposes. Walls exposed to fire on more than one face are to be regarded as columns (see 7.5). Table 50 - Fire resistance of siliceous aggregate concrete walls containing at least 1,0 % of vertical reinforcement and exposed to fire on one face only 1
2
3
4
5
6
7
Minimum dimension of concrete mm Description of applied finish
Fire resistance h
None . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cement or gypsum plaster on exposed face Vermiculite/gypsum plaster*) or sprayed asbestos, 15 mm thick, on exposed face . .
4
3
2
1,5
1
0,5
180 180
150 150
100 100
100 100
75 75
75 75
125
100
75
75
65
65
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
7.6.2 Plain concrete walls From the limited data available, the fire resistance of plain siliceous aggregate concrete walls can be taken as follows: - Concrete, 150 mm thick: 1 h; - Concrete, 175 mm thick: 1,5 h.
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SABS 0100-1 Ed. 2.2
Annex A (informative)
Methods of checking for compliance with serviceability criteria by direct calculation A.1 Analysis of structure for serviceability limit states A.1.1 Loads See 3.3.4.1.
A.1.2 Moments and forces In general, it will be sufficiently accurate to use an elastic analysis to assess the moments and forces in elements subjected to their appropriate loadings for the serviceability limit states. Where a single value of stiffness is used to characterize an element, the stiffness of the element may be based on the concrete section. In this case, it is likely to provide a more accurate picture of the moment and force fields than will the use of a cracked transformed section, even though calculation shows the elements to be cracked. Where more sophisticated methods of analysis are used, in which variations in properties over the length of elements can be taken into account, it will frequently be more appropriate to calculate the stiffness of highly stressed parts of elements on the basis of a cracked transformed section.
A.1.3 Material properties For checking serviceability limit states, the modulus of elasticity of the concrete should be taken as the mean value given in table C.1, appropriate to the characteristic strength of the concrete. The modulus of elasticity may be corrected for the age of loading if this is known. Owing to the large range of values for the modulus of elasticity that can be obtained for the same cube strength, it might be appropriate to consider either calculating the behaviour of the element (by using moduli at the end of the ranges given in table C.1 to obtain an idea of reliability of the calculation) or having tests done on the actual concrete to be used. For appropriate values of creep and shrinkage, refer to annex C.
A.2 Calculation of deflection A.2.1 General A.2.1.1 When the deflections of reinforced concrete elements are calculated, note that there are a number of factors that may be difficult to allow for in the calculation but that can have a considerable effect on the reliability of the result. The following points should be taken into consideration: a)
estimates of the restraints provided by supports are based on simplified and often inaccurate assumptions;
b)
the precise loading, or the part of it that is of long duration, is unknown; the self-weight, which is known to within quite close limits, is the major factor determining the deflections, since this largely
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SABS 0100-1 Ed. 2.2 governs the long-term effects; lack of knowledge of the precise imposed load is not likely to be a major cause of error in deflection calculations; for the proportion of imposed loading that may be considered to be permanent and that will influence the long-term behaviour, see 3.3.4.1; c)
lightly reinforced elements may well have a working load that is close to the cracking load for the element; considerable differences will occur in the deflections, depending on whether the element has or has not cracked;
d)
the effects of finishes and partitions on deflection are difficult to assess and are often ignored; if a partition is built on top of a beam where there is no wall built up to the underside of the beam, the long-term deflection will cause the beam to creep away from the partition; the partition may be left spanning as a deep beam that will apply significant loads at its ends only to the supporting beam; thus, if a partition wall is built over the whole span of a beam with no major openings near its centre, its mass may be ignored in the calculation of long-term deflections of the supporting beam; the suitable approach for assessing the magnitude of this effect is to calculate a likely maximum and minimum deflection and to take the average.
A.2.1.2 Any method of calculation that can be demonstrated to yield results of acceptable accuracy can be used, provided that points such as those listed in A.2.1.1 have been correctly accounted for, and may be logically applied over a wide range of problems. The approach used in the method of calculation given in A.2.3 is to assess the curvatures of sections under the appropriate moments (as in A.2.2) and then calculate the deflections from the curvatures. The method of calculation given in A.2.4 is an alternative to the method given in A.2.3 and deals additionally with the deflection of fully and partially prestressed concrete elements. Shrinkage deflection may be calculated as in A.2.5.
A.2.2 Calculation of curvatures A.2.2.1 Sets of assumptions The curvature of any section may be calculated by employing whichever of the following sets of assumptions, A or B, gives the larger value. Set of assumptions A applies to a section that is cracked under the loading under consideration, while set of assumptions B applies to an uncracked section.
A.2.2.2 Set of assumptions A (section cracked) A.2.2.2.1 Strains are calculated on the assumption that plane sections remain plane. A.2.2.2.2 The reinforcement, whether in tension or in compression, is assumed to be elastic. Its modulus of elasticity may be taken as 200 GPa. A.2.2.2.3 The concrete in compression is assumed to be elastic. Under short-term loading, the modulus of elasticity may be taken as that given in 3.4.2.1. Under long-term loading, an effective modulus may be taken as having a value of 1/(1 + Φ) times the short-term modulus, where Φ is the appropriate creep factor (see C.2). A.2.2.2.4 Stresses in the concrete in tension may be calculated on the assumption that the stress distribution is triangular, having a value of zero at the neutral axis and a value of 1 MPa at the centroid of the tension steel in the short term, reducing to 0,55 MPa in the long term.
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SABS 0100-1 Ed. 2.2 A.2.2.3 Set of assumptions B (section not cracked) The concrete and the steel are both considered to be fully elastic in tension and in compression. The modulus of elasticity of the steel may be taken as 200 GPa and that of the concrete as specified in A.2.2.2.3, both in compression and in tension.
A.2.2.4 The equation of the curvature These assumptions are illustrated in figure A.1. In each case the curvature can be obtained from the following equation: f fs 1 c xEc rb (dx) Es where 1 rb fc
is the curvature at midspan or, for cantilevers, at support section; is the design service stress in concrete;
Ec is the short-term modulus of concrete; fs
is the estimated design service stress in tension reinforcement;
d
is the effective depth of section;
x
is the depth to neutral axis; and
Es is the modulus of elasticity of reinforcement. For set of assumptions B, the following alternative may be more convenient: 1 M Ec I rb where M is the moment at section under consideration; and I
is the second moment of area.
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SABS 0100-1 Ed. 2.2
NOTE – h d x fc fs As Ec Es
is the overall depth of section; is the effective depth of section; is the depth from compression face to neutral axis; is the maximum compressive strength in concrete; is the tensile strength in reinforcement; is the area of reinforcement; is the modulus of elasticity of concrete; and is the modulus of elasticity of reinforcement.
Figure A.1 — Assumptions made in calculating curvatures
A.2.2.5 Total long-term curvature In the assessment of the total long-term curvature of a section, the following procedure may be adopted: a)
calculate the instantaneous curvatures under the total load and under the permanent load;
b)
calculate the long-term curvature under the permanent load;
c)
to the long-term curvature under the permanent load, add the difference between the instantaneous curvatures under the total and permanent loads; and
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SABS 0100-1 Ed. 2.2 d)
to this curvature, add the shrinkage curvature calculated from the following formula: S 1 cs e s I rcs
where 1 rcs
is the shrinkage curvature;
cs
is the free shrinkage strain;
e
is the modular ratio =
Es
is the modulus of elasticity of reinforcement;
Es Eeff
;
Eeff is the effective modulus of elasticity of concrete (which can be taken as Ec /(1 + )); Ec
is the short-term modulus of the concrete;
is the creep factor;
I
is the second moment of area of either cracked or gross section, depending on whether curvature due to loading is derived from set of assumptions A or set of assumptions B; and
Ss
is the first moment of area of reinforcement about centroid of cracked or gross section, whichever is appropriate.
A.2.3 Calculation of deflection from curvatures The deflected shape of an element is related to the curvatures by the following equation: 2 1 d 2 rx dx
where 1 rx
is the curvature at x; and
is the deflection at x.
Deflections may be calculated directly from this equation by calculation of the curvatures at successive sections along the element and the use of a numerical integration technique such as that proposed by Newmark. Alternatively, the following simplified approach may be used: The deflection is calculated from the equation = Kl2
1 rb
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SABS 0100-1 Ed. 2.2 where is the effective span of element;
l 1
is the curvature at midspan or, for cantilevers, at support section; and
rb K
is a coefficient that depends on shape of the bending moment diagram. (See figure A.2.)
As the calculation method does not describe an elastic relationship between moment and curvature, deflections under complex loads cannot be obtained by summation of the deflections obtained by separate calculation for the constituent simpler loads. A value of K appropriate to the complete load should be used. If figure A.2 is used to assess the value of K by superposition, it may be assumed that the maximum deflection of a beam occurs at midspan, without serious errors being introduced. The calculation of the deflection of cantilevers requires very careful consideration whether the cantilever is rigidly fixed and is therefore horizontal at the root, or whether the root of the cantilever is caused to rotate owing to the loadings on the cantilever itself, or on other elements to which the cantilever is connected. If this root rotation is , the deflection of the tip of the cantilever will be decreased or increased by an amount l. In general it is recommended that the effective span of the cantilever (as defined in 4.3.1.4) be used. Deflection of slabs is probably best dealt with by using the ratios of span to effective depth. However, if the calculation of the deflections of a slab is essential, it is suggested that the following procedure be adopted: A strip of slab of unit width is chosen such that the maximum moment along it is the maximum moment of the slab, i.e. in a rectangular slab, a strip spanning across the shorter dimension of the slab connecting the centres of the longer sides. The bending moments along this strip should preferably be obtained from an elastic analysis of the slab, but may be assessed approximately by taking 70 % of the moments used for the collapse design. The deflection of the strip is then calculated as though the strip were a beam. This method will be slightly conservative.
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SABS 0100-1 Ed. 2.2
Figure A.2 — Values of K for various bending moment diagrams
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SABS 0100-1 Ed. 2.2 A.2.4 Calculation of deflection (an alternative to the method given in A.2.3) A.2.4.1 Reinforced concrete elements A.2.4.1.1 In the absence of more reliable information, it is recommended that the immediate deflection ∆i at the midspan of the member due to applied characteristic load be calculated as:
∆i = KMs
l2 E c e
where
∆i
is the immediate deflection;
Ms
is the max. moment of permanent load at support for cantilevers, elsewhere at midspan;
l
is the effective span of member (in terms of 4.3.1.4);
Ec
is the modulus of elasticity of concrete at instant of loading;
Ie
is the effective second moment of area (see equation (22)); and
K
is the deflection coefficient that depends on the shape of the bending moment diagram.
Note that for two-way slabs, all relevant parameters/notation refer to the short span. Bending moments in the element should be determined by moment distribution, computer methods or any other suitable method in accordance with A.1.2. The second moment of area Ie should incorporate the degree of cracking in the element and can be approximated by the following formula, which also accounts for tension stiffening of the concrete:
Ie
=
Mcr 3 Ma
but not exceeding Ig
180
Ig + [1 -
Mcr 3 Ma
] Icr
(22)
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SABS 0100-1 Ed. 2.2 where Mcr is the cracking moment of element, such that: Mcr =
fr
g
yt
and fr
is the modulus of rupture, such that: fr
= 0,65 f cu
for unrestrained beams and slabs; and
fr
= 0,30 f cu occur;
for restrained beams and slabs where pre-loading cracking is likely to
Ma is the maximum moment in the element corresponding with the deflection situation under consideration; Icr
is the moment of the inertia of the cracked transformed section;
Ig
is the moment of inertia of concrete section (ignoring reinforcement); and
yt
is the distance from centroidal axis of concrete section (ignoring reinforcement), to extreme fibre in tension.
For continuous elements, the effective moment of inertia may be taken as the average of the Ie values for the critical positive moment and negative moment sections. For prismatic elements, the effective moment of inertia may be taken as Ie obtained at midspan for simple and continuous spans, and at support for cantilevers. A.2.4.1.2 Long-term creep deflection ∆ shall be calculated by multiplying the immediate deflection by a factor λ, such that:
∆
=
λ∆i
(23)
where
∆
is the long-term creep deflection;
∆i
is the immediate deflection;
λ
is 1 + xi Φ;
xi
is the ratio of neutral axis depth to effective depth of cracked element; and
Φ
is the creep strain divided by the initial strain; Φ is the creep factor considering age of concrete at loading, humidity, surface-to-volume ratio, etc.
Figure C.1 can be used as a guide in this regard.
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SABS 0100-1 Ed. 2.2 A.2.4.1.3 Where compression reinforcement is present,
shall be substituted by
where
|
p
=
1
p 2
; and
Amdt 2, Mar. 2000
is the ratio of compression steel area to tension steel area.
A.2.4.1.4 The permanent loads to consider for long-term deflections shall be in accordance with SABS 0160.
A.2.4.2 Fully and partially prestressed concrete elements The same procedure as for reinforced concrete elements can be followed except that a) for fully prestressed (uncracked) concrete elements, Ie = Ig; and b) for partially prestressed concrete elements, cognizance should be taken of the fact that the centre of gravity of the section does not coincide with the element neutral axis owing to the presence of the axial prestress force. Short-term deflections can be based on Ie as calculated from equation (22). For long-term deflections, the ratio of the neutral axis depth to the effective depth of the cracked element xi is required in order to use equation (23). This can be determined by considering strain compatibility and equilibrium of forces in the element, or by using the following empirical equation:
xi
=
Mcr 2,5 M1
xg 1
(Mcr)2,5 M1
xcr
where xi
is the ratio of neutral axis depth to effective depth of partially prestressed element;
xg
is the ratio of neutral axis depth to gross concrete depth;
xcr
is the ratio of neutral axis depth to fully cracked element depth, at the section where deflection is under consideration;
Mcr is as in equation (22); and M1 is the moment causing deflection relative to zero curvature situation.
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SABS 0100-1 Ed. 2.2 A.2.5 Calculation of shrinkage deflection The shrinkage deflection may be calculated as follows:
s
s l 2
= kskcs
h
where ks
is 0,5 for cantilevers; is 0,125 for simply supported members; is 0,086 one end continuous; is 0,063 both ends continuous;
s
is the free shrinkage strain of concrete, for instance from figure C.2;
kcs
is
(1 ) )
0,7
|
< 1 > 0 for uncracked members;
|
with
1
)
[1 0,11(3 )2 ]
kcs
is
l
is the effective span of member (in terms of 4.3.1);
Ý
=
100As
|
< 1 > 0,3 for fully cracked members; and
| | | |
< 3,
bd
|
Ý
=
100As bd
|
,
Ý < 1, Ý
As
is the area of bonded steel.
| Amdt 1, Apr. 1994
A.3 Calculation of crack width A.3.1 General A.3.1.1 Since the bar spacing rules given in 4.11.8 ensure that cracking is not serious in the worst likely practical situation, it will almost always be found that wider bar spacing can be used if the crack widths are checked explicitly. This will be true particularly for fairly shallow elements. A.3.1.2 The widths of flexural cracks at a particular point on the surface of an element depend primarily on three factors:
183
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SABS 0100-1 Ed. 2.2 a) the proximity of reinforcing bars perpendicular to the cracks to the particular point being considered; b) the proximity of the neutral axis to the particular point being considered; and c) the average surface strain at the particular point being considered.
A.3.1.3 The formula in A.3.2 gives a relationship between crack width and these three principal variables, which gives acceptably accurate results in most normal design circumstances. However, use the formula with caution in elements subjected dominantly to an axial tension.
A.3.1.4 Remember that cracking is a semi-random phenomenon and that an absolute maximum crack width cannot be predicted. The formula is so designed that an acceptably small number of cracks in a structure will exceed the predicted width. Do not, therefore, regard an occasional crack slightly larger than the predicted width as cause for concern. However, should a significant number of the cracks in a structure exceed the predicted width, seek reasons other than the statistical nature of the phenomenon to explain their presence.
A.3.2 Formula for assessing crack widths A.3.2.1 Provided that the strain in the tension reinforcement is limited to 0,8fy/Es (fy is characteristic strength of reinforcement and Es is modulus of elasticity of reinforcement), the design surface crack width, which shall not exceed the appropriate value given in 3.2.3.3, may be calculated from the following equation: 3acr m
|
w= 1 % 2
(acr & c min) h&x
Amdt 1, Apr. 1994
where w
is the design surface crack width;
acr
is the distance from the point being considered to the surface of the nearest longitudinal bar;
m
is the average steel strain at the level where cracking is being considered, calculated allowing for stiffening effect of concrete in tension zone, and obtained from equation (24);
cmin
is the minimum cover to tension steel;
h
is the overall depth of member; and
x
is the depth of neutral axis found from analysis to determine 1 (see below).
The average steel strain m may be calculated on the basis of the assumptions given in A.2.2. Alternatively, as an approximation, it will normally be satisfactory to calculate the steel stress on the basis of a cracked section, and then to reduce this by an amount equal to the tensile force generated by the stress distribution (defined in A.2.2.2.4) acting over the tension zone divided by the steel area. For a rectangular tension zone, this gives:
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SABS 0100-1 Ed. 2.2 Jm
J1
bt (h x) (a ) x) 3 Es As (d x)
(24)
where m is the average steel strain; 1
is the strain at the level being considered, calculated ignoring stiffening effect of concrete in tension zone;
bt
is the width of section at centroid of tension steel;
h
is the overall depth of element;
x
is the depth of neutral axis;
Es is the modulus of elasticity of reinforcement; As is the area of tension reinforcement; d
is the effective depth; and
a is the distance from compression face to point at which crack width is being calculated. When the whole section is in tension, an effective value of (h - x) can be estimated by interpolation between the following limiting conditions: a) where the neutral axis is at the least compressed face, ( h - x) = h (i.e. x = 0); and b) for axial tension (h - x) = 2h. A negative value for m indicates that the section is uncracked.
A.3.2.2 In the assessment of the strains, the modulus of elasticity of the concrete should be taken as half the instantaneous value. A.3.2.3 Where it is expected that the concrete may be subject to abnormally high shrinkage strains (>0,0006), increase m by adding 50 % of the expected shrinkage strain.
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SABS 0100-1 Ed. 2.2
Annex B (informative)
Movement joints B.1 General Many factors influence the tendency of concrete to crack, and the limitation of such cracking is also influenced by many factors, probably the most important of which is the proper provision of adequate reinforcement. However, there are cases where the most appropriate or indeed the only control measure is a movement joint.
B.2 Need for movement joints B.2.1 In common with all other structural materials, concrete expands when heated and contracts when cooled; it also expands when wetted and shrinks when dried. It also undergoes other strains owing to the hydration of the cement and other properties of the material itself and of its constituent parts. If these expansions and contractions are restrained, stresses will occur that can be of sufficient magnitude to cause immediate cracking of the concrete, or cracking will occur later owing to fatigue failure resulting from long-term repetition of the stresses. Creep of the concrete over a long period can in some cases reduce stresses due to restraint, but generally this should not be relied upon. Differential settlements of foundations due, for example, to mining subsidence might also need to be provided for. As these factors may cause unsightly cracking, damage to finishes, and even structural failure, the possibilities and effects of such cracking should be properly investigated in relation to the design, reinforcement and form of the element or structure concerned and in the light of published information. If it is then found necessary to prevent or limit the effects of such potential cracking, movement joints should be provided at predetermined locations.
B.2.2 Some indication of the possible magnitude of the movements to be dealt with in a concrete structure may be gained from the examples given below. B.2.2.1 The average coefficient of thermal expansion of concrete is about 10-5/1 °C; thus a 33 °C change in temperature could cause a difference in length of approximately 10 mm in a concrete element of length 30 m. If this change in length were to be prevented by complete restraint of the element, it would cause a stress of about 7 MPa in an unreinforced concrete element having a modulus of elasticity of 20 GPa. If such stress were tensile, and superimposed upon other already existing tensile stresses, cracking would occur. (If, however, the concrete were to be reinforced, the distribution of the cracking would be controlled by the amount, form and distribution of the reinforcement, which might even reduce the crack width and spacing to the extent that no harmful consequence would be caused.)
B.2.2.2 Drying shrinkage strains may be roughly 500 x 10-6. In thin reinforced sections, this represents an unrestrained shrinkage of about 1,5 mm per 3 m length of a concrete element. If this change in length were to be prevented, a tensile stress of about 10 MPa would occur. (See also annex C.3.)
B.2.2.3 Creep of concrete under stress tends to reduce the maximum stresses arising from the restraint of movements of the types referred to in B.2.2.1 and B.2.2.2, the degree of reduction depending on, among other factors, the rate of change of the stresses. Creep is a long-term process and if the stresses change rapidly, e.g. because the cross-section of the element is small enough to permit its temperature change or shrinkage to occur in a relatively short time, it has a negligible effect on reducing the stresses.
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SABS 0100-1 Ed. 2.2 B.2.3 However, creep of the concrete can itself create strains that could lead to harmful and unsightly effects if no movement joints were to be provided. For example, creep of the concrete can cause deflections of beams to increase over a long period under sustained loading. Unless suitable movement joints are provided between floors or roofs and partitions, these deflections can lead to heavy loads being imposed upon the partitions, which, if of a non-load-bearing type, may then suffer severe cracking. (See also annex C.2.)
B.3 Types of movement joints Movement joints may be any one of the types given below.
B.3.1 Contraction joint A contraction joint is a joint with a deliberate discontinuity but no initial gap between the concrete on both sides of the joint, the joint being intended to permit contraction of the concrete. A distinction should be made between a complete contraction joint in which both the concrete and the reinforcement are interrupted, and a partial contraction joint in which only the concrete is interrupted but the reinforcement runs through.
B.3.2 Expansion joint An expansion joint is a joint with complete discontinuity in both reinforcement and concrete and intended to accommodate either expansion or contraction of the structure. In general, such a joint requires the provision of a sufficiently wide gap between the adjoining parts of the structure, to permit the occurrence of the amount of expansion expected. Design of the joint so as to incorporate sliding surfaces is not, however, precluded and may sometimes be advantageous.
B.3.3 Sliding joint A sliding joint is a joint with complete discontinuity in both reinforcement and concrete. Special provision is made at the joint, to facilitate relative movement in the plane of the joint.
B.3.4 Hinged joint A hinged joint is a joint specially designed and constructed to permit relative rotation of the elements at the joint. This type of joint is usually required to prevent the occurrence of reverse moments or of undesirable restraint, for example in a three-hinged portal.
B.3.5 Settlement joint A settlement joint is a joint intended to permit adjacent elements or structures to settle or deflect relative to each other in cases, for example, where movements of the foundations of a structure are likely to take place as a result of mining subsidence. The relative movements may be large. NOTE - It may be necessary to design a joint to fulfil more than one of the requirements given in B.3.1 to B.3.5.
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B.4 Provision of joints B.4.1 The risk of cracking due to thermal movement and shrinkage may be minimized if the changes in temperature and moisture content to which the concrete of the structure is subjected are limited. The extent to which this can be done in the completed structure will depend very largely on its type and environment, ranging from the underground basement, where the temperature and humidity are relatively constant, to the uninsulated elevated structure, where the temperature and humidity are close to the atmospheric temperature and humidity. Furthermore, in modern buildings, the effects of central heating on both the temperature and moisture content of the structure, combined with the relatively low thermal storage capacity of buildings clad with low-density curtain walls, may give rise to more onerous thermal and humidity conditions than in older, heavier, relatively unheated buildings. Thus, the investigation of the necessity of providing movement joints is becoming more important.
B.4.2 Cracking can be minimized by reducing the restraints on the free movement of the structure, and the control of cracking normally requires the subdivision of a structure into suitable lengths separated by the appropriate movement joints.
B.4.3 The effectiveness of movement joints in controlling cracking in a structure will also depend upon their precise location; this is frequently a matter of experience, and the location of movement joints may be characterized as the places where cracks would otherwise most probably develop, e.g. at abrupt changes of cross-section. B.4.4 The location of all movement joints should be clearly indicated on the drawings, both for individual elements and for the structure as a whole. In general, movement joints in the structure should pass through the whole structure in one plane.
B.5 Design of joints A movement joint should fulfil all necessary functional requirements. It should possess the merits of simplicity and freedom of movement, yet still retain the other appropriate characteristics necessary, e.g. weatherproofness, fire resistance, corrosion resistance, durability and sound insulation. The design should also take into consideration the degree of control and workmanship and the tolerances likely to occur in the actual structure of the type being considered. Where joints are of a filled type, they may, in appropriate cases, be filled with a building mastic.
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Annex C (informative)
Elastic deformation of concrete C.1 Modulus of elasticity C.1.1 The modulus of elasticity of concrete is influenced by the elastic properties of the aggregate and, to a lesser extent by the aggregate/cement ratio, condition of curing, type of cement and age of the concrete. In the case of concrete made from natural aggregates and having a density of 2 300 kg/m3 or more, the static or dynamic modulus of elasticity may be taken from table C.1 for concretes of various compressive strengths.
C.1.2 If a more accurate figure is required for particular materials and a particular mix, tests should be carried out. Concrete made from a few particular sources of aggregate may have a modulus of elasticity substantially outside the range given in table C.1. The use of these materials may be permitted, provided that the appropriate value for elastic modulus obtained from tests is used in design calculations.
C.1.3 Where, in special circumstances, an as-accurate-as-possible assessment of actual behaviour is required, it will be necessary to consider possible variations in the value for modulus of elasticity. Guidance on this follows, but it is emphasized that the value chosen in any particular case will depend on the importance of the estimate and why it is needed. The mean values of static modulus of elasticity for normal-density concrete in table C.1 are derived from the following equation: Ec,28 = Ko + 0,2 fcu,28 where Ec,28
is the static modulus of elasticity at 28 d;
fcu,28
is the characteristic cube strength, in MPa; and
Ko
is a constant closely related to the modulus of elasticity of the aggregate (taken as 20 kN/mm2 for normal-density concrete). The variety of factors affecting the prediction and determination of the elastic modulus of concrete with specific reference to local aggregates and cements are discussed in the documents given in (a), (d) and (e) of annex E.
The modulus of elasticity of concrete Ec at an age t may be derived from the following equation: Ec,t = Ec,28 (0,4 + 0,6 fcu,t/fcu,28)
(25)
where t
> 3 d;
Ec,28
is the static modulus of elasticity at 28 d, obtainable from table C.1; and
fcu
is the characteristic strength of concrete.
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SABS 0100-1 Ed. 2.2 Values of fcu,t/fcu,28 for use in equation (24) can be obtained from table 2. This table shows that, on average, there is likely to be a gain of strength beyond 28 d (this will lead to a more realistic assessment of the modulus of elasticity). It should be noted that there is a difference here from the main body of this part of SABS 0100 where no increase in strength beyond 28 d is permitted in satisfying limit state requirements. A smaller increase in strength will occur with small structural members that are exposed to a dry environment after initial curing. Where calculations of deflection or deformation are to be made, the reliability of the estimate of the static modulus of elasticity will depend on the precision required from the calculation. Where deflections are of great importance, tests should be carried out on concrete made with the aggregate to be used in the structure. In other cases, experience with a particular aggregate, backed by general data, will often provide a reliable value for Ko, and hence for Ec,28, but with unknown aggregates, it would be advisable at the design stage to consider a range of values for Ec,28, as given in table C.1. In the case of low-density aggregate concrete, the values of the static modulus in table C.1 should be multiplied by (w/2400)2 where w is the density of low-density aggregate concrete (in kilograms per cubic metre). It may be more convenient to use the dynamic modulus method of test to obtain an estimated value for the static modulus of elasticity, using the formula Ec = 1,25 Ecq - 19 where Ecq is the dynamic modulus of elasticity obtainable from table C.1. Such an estimated value will generally be correct to within 5 GPa. Table C.1 - Modulus of elasticity of normal-density concrete 1 Characteristic strength fcu, MPa
2
3
4
5
Static modulus Ec,
Dynamic modulus Ecq,
GPa
GPa
Mean value
Typical range
Mean value
Typical range
20 25 30
25 26 28
21-29 22-30 23-33
35 36 38
31-39 32-40 33-43
40 50 60
31 34 36
26-36 28-40 30-42
40 42 44
35-45 36-48 38-50
C.2 Creep and shrinkage The final (30-year) creep strain in concrete, εcc, can be predicted from the formula εcc
=
stress Φ Et
where Et
is the modulus of elasticity of concrete at age of loading t; and
Φ
is the creep factor obtainable from figure C.1.
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Figure C.1 — Effects of relative humidity, age of concrete at loading and section thickness upon creep factor The effective section thickness is defined in figure C.1 for uniform sections as twice the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water or by sealing, the effective section thickness should be taken as 600 mm. It can be assumed that about 40 %, 60 % and 80 % of the final creep develops during the first month, first 6 months and first 30 months under load respectively, when concrete is exposed to conditions of constant relative humidity. Creep is partly recoverable with a reduction in stress. The final creep recovery after one year is approximately 0,3 times stress reduction/Eu, where Eu is the modulus of elasticity of the concrete at the age of unloading.
C.3 Drying shrinkage An estimate of the drying shrinkage of plain concrete may be obtained from figure C.2. Recommendations for effective section thickness are given in C.2.
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SABS 0100-1 Ed. 2.2 Figure C.2 relates to concrete of normal workability made without water-reducing admixtures; such concrete will have an original water content of about 190 elm3.Where concrete is known to have a different water content, shrinkage may be regarded as proportional to water content within the range
10 y e a r ihrinkaqe x106
I
i month zhrinkage x10' Effective section thickness ") mm
20
30
40
50
60
70
80
90
100
Ambient r e l a t i v e hum~dity, % 41
See C.2
Figure C.2 - Drying shrinkage of normal-density concrete
The shrinkage of plain concrete is primarily dependent on the relative humidity of the air surrounding the concrete, on the surface area from which moisture can be lost relative to the volume of concrete, and on the mix proportions. It is increased slightly by carbonation and self-desiccation and is reduced by prolonged curing. In general, all factors that influence creep will apply equally to shrinkage. It should be noted that where detailed calculations are being made, stresses and relative humidities may vary considerably during the lifetime of the structure, and appropriate judgements should be made.
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Annex D (informative)
The design of deep beams D.1 General Deep beams are defined as prismatic members, generally straight and of constant cross-section having a ratio of effective span to overall depth of less than 2 and such that the assumption that plane sections remain plane in bending does not apply. In the case of continuous beams, the transition to a deep beam for decreasing span to depth ratios is gradual and depends on the distribution of loading, so that any given ratio is approximate if applied generally. The effective span of a simply supported deep beam may be assumed to be the distance between centre-lines of supports provided that this distance does not exceed 1,15 times the span between the faces of supports, in which case the effective span is to be taken as 1,15 times the clear span. In the case of continuous beams, the above-mentioned definition of the effective span applies if the effective spans for this purpose are taken as the approximate distances between the points of contraflexure. Alternatively, if span lengths are calculated as for simply supported beams, the span to depth ratio would be approximately 2,5 to 3. In the case of cantilevers, the ratio would be approximately 1.
D.2 Design and analysis Deep beams may be designed and analysed by means of any of the following: a) linear analysis based on the theory of elasticity (see D.2.1); or b) procedures such as the application of statically admissible stress fields in accordance with the lower bound theorem of limit analysis by analogy with the behaviour of equivalent truss or lattice structures consisting of struts and ties or tied arches (all preferably following the elastic field) (see D.2.2); or c) non-linear analysis (see D.2.3); or d) methods using the results of experimental tests on models of reinforced concrete or other suitable materials or on prototypes or based on the extrapolation of published results of experimental or theoretical work by reputable persons.
D.2.1 Linear analysis The theory of elasticity may be applied assuming values of Poisson's ratio of 0,0 to 0,2. In most cases, only numerical solutions are suitable (such as, for example, finite differences, finite-element-methods, or boundary element-methods). The analysis defines the fields of principal stresses and deformations. High stress concentrations (for instance, those at the corner of possible openings) may be reduced by cracking effects. The linear analysis is valid both for serviceability and ultimate limit states. The analysis in the ULS requires a correct detailing of the reinforcement, to withstand the resultant forces in tensile zones in the concrete and to satisfy equilibrium conditions.
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SABS 0100-1 Ed. 2.2 D.2.2 Equivalent truss analogy (analysis by admissible stress fields) If a stress field is chosen which satisfies the equilibrium conditions, a lower bound solution of limit analysis is considered. For the structure and its loads, an equivalent truss may be investigated, consisting of concrete struts and arches as compressive members and of steel ties formed by the reinforcement as tensile elements and their connections (nodes). Any equilibrium model may be applied for verifying the ULS and also for the SLS, provided that the evaluated stress distribution is close to the results of the linear analysis (see figures D.1 and D.2). A similar approach is also valid for continuous beams. The equilibrium model should preferably be based on the dominating load pattern but where point loads and distributed loads have similar influences or dominate at various times, a more complex model being a combination of the extreme patterns is required (see figure D.3). The above-mentioned nodes are defined as the volumes of concrete contained within the intersections between compression fields of struts, in combination with anchorage forces or external compressive forces (imposed loads or support reactions) or both. The nodes should be so dimensioned that all forces are anchored and balanced safely.
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Figure D.1 — Equivalent truss resisting point loads
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Figure D.2 — Equivalent arch resisting UD load and self-weight
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Figure D.3 — Equivalent truss resisting unequal point loads A > B
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SABS 0100-1 Ed. 2.2 The geometry of the node region and the arrangement of reinforcement in it should be consistent with the model on which the design of the structure is based and with the applied forces. Thereby the equilibrium conditions should be fulfilled. Nodes should be verified accordingly by: - verification of the stresses from the compressive struts in the node in accordance with D.2.4 ; and - verification of the anchorages of ties. The anchorage of bars should comply with 4.11.6. The anchorage length will be assumed to begin at the section where the transverse compressive stress trajectories of a strut meet the anchored bar and are deviated. The anchorage bar should extend at least over the whole length of the compression field which is deviated by it. Transverse tensile forces from bond actions and minor non-uniformities of applied strut stresses should normally be covered by structural reinforcement (e.g. stirrups) arranged near the surfaces.
D.2.3 Non-linear analysis For a more refined analysis, non-linear stress-strain relations may be taken into account by applying numerical methods as for two-dimensional plane structures. The results of the analysis may be used for both serviceability and ultimate limit states.
D.2.4 Bearing stresses at nodes The design bearing stress is given by: fb1 = ßfcd where
is 1,0 for nodes where only compression struts meet; is 0,8 for nodes where main tensile bars are anchored; ß is the least of b1/a1 or b2/a2 or 4 where a1 and a2 are the dimensions of the loaded area (see figure D.4); b1 and b2 (symetrically to the loaded area) are determined from limitations to the dispersion of the stresses (figure D.4); and fcd is the design strength of concrete. If an additional horizontal force H is acting at a support (figure D.4(c)), the bearing stress may be calculated from the following formula:
c =
198
F2 H2 < fb1 Fa1a2
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Figure D.4 — Loaded area Transverse tension (see figure D.4(a)) may be calculated using the formula: T
1 b1 a1 b1 4
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Annex E (informative)
Bibliography The information contained in this part of SABS 0100 is considered adequate for the design of the majority of buildings. For buildings, structures or elements that are not adequately covered or where special conditions apply or where additional information is desired by the designer, the following publications should be consulted: a) Alexander, MG. Prediction of elastic modulus for design of concrete structures. The Civil Engineer in South Africa, June 1985, vol. 27, No. 6, p. 313-324. b) Alexander, MG and Davis, DE. Properties of aggregates in concrete, Part 1. Hippo Quarries Technical Publication, 1989. 44p. c) Alexander, MG and Davis, DE. Properties of aggregates in concrete, Part 2. Hippo Quarries Technical Publication, 1992. 48p. d) Alexander, MG and Davis, DE. The influence of aggregates on the compressive strength and elastic modulus of concrete. The Civil Engineer in South Africa, May 1992, Vol. 34, No. 5, p. 161-170. e) Chana, PS. Some aspects of modelling the behaviour of reinforced concrete under shear loading. Cement and Concrete Association Technical Report 543, July 1981. f) Cross, MG. A proposed parametric design model for shear in reinforced concrete. The Civil Engineer in South Africa, April 1987, vol. 29, No. 4, p. 127-134. g) Goldstein, AE. Prestressed concrete flat slabs. (In course of publishing.) h) Kani, Huggins and Wittkopp (ed.). Kani on shear in reinforced concrete. Department of Civil Engineering, University of Toronto, 1979. i) Kemp, AR, Milford, RV and Laurie, JAP. Proposals for a comprehensive limit states formulation for South African structural codes. The Civil Engineer in South Africa, September 1987, vol. 29, No. 9, p. 351-360. j) Scholz, H. Proposed design provisions for reinforced concrete columns. The Civil Engineer in South Africa, May 1988, vol. 30, No. 5, p. 229-238. k) BS 8007, Design of concrete structures for retaining aqueous liquids.
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