BFC32803 Reinforced Concrete Design II
Frame Analysis Dr. Zainorizuan Mohd Jaini
[email protected]
Learning Outcome At the end of this chapter, chapter, students should be able to: 1) Analys Analyse e the respon responses ses of of build building ing (shear (shear force force and bendin bending g moment) subjected to combined vertical actions and wind load. (C4-PLO4) 2) Manipu Manipulat late e struct structura urall design design proc process esses es to comp complet lete e the assigned project. (P4-PLO2) 3) Repor Reportt design design work works s which which compr comprise ise of of ideas ideas and and prob problem lem solving through suitable tools or methods (A3-PLO3) BFC32803 Reinforced Concrete Design II
Introduction The
building structure is 3D, comprising floor slabs, beams, columns and footings, which monolithically connected and act integrally to resist vertical/lateral loads.
In
the design, it has to analyze the structure subjected to all probable combinations of loads, considering the ultimate limit state.
Once
the bending moment, shear force etc. were obtained, reinforcements can be designed according to the standard.
Generally,
3D wide frame analysis is the most accurate method to analyse the frame building
BFC32803 Reinforced Concrete Design II
Introduction
3D frame which consist of slabs, beams and column
BFC32803 Reinforced Concrete Design II
Introduction 3D
frame is complex and need to be carried out using relevant computer software such as StaadPro, ESTEEM, ETABS, etc.
However,
in many cases the slabs are analyzed separately.
Thus,
the analysis may be simplified to appropriate sub-frame, consist only beams and columns. BFC32803 Reinforced Concrete Design II
Introduction However,
in many cases the slabs are analyzed separately.
Thus,
the analysis may be simplified appropriately sub-frame, consist only beams and columns.
3D frame which consist of slabs, beams and column
simplified
3D frame consist only beams and columns
BFC32803 Reinforced Concrete Design II
Introduction In
order to simplify the analysis, the 3D structure is generally divided into a series of independent parallel 2D plane frames.
View-X
View -Y BFC32803 Reinforced Concrete Design II
Sub-Frames 2D
plane frame can be further simplified into 3 level sub-frames:
i)
Complete sub-frame The frame consists of all beams at each level with columns top and bottom of beams. Moments at columns and beams are tabulated by analyzing the complete sub-frame.
ii)
Simplified sub-frame The frame consists of a selected beam with columns and neighbouring beams at both sides of selected beam.
iii) Simplified sub-frame at point The frame consists of a selected point or node with columns at top and bottom, and neighbouring beams coming into the point. BFC32803 Reinforced Concrete Design II
Sub-Frames 2D
plane frame >>> complete sub-frame: Roof Second floor
A
B
C
D
E
D
E
First floor
Complete 2D Frame
A
B
C
Sub-frame at second floor BFC32803 Reinforced Concrete Design II
Sub-Frames Complete
sub-frame >>> Simplified sub-frame:
Roof Second floor
A
B
C
D
E
A
B
First floor
Complete 2D Frame
A
B
C
Simplified sub-frame beam BC
D
C
Simplified sub-frame beam AB
BFC32803 Reinforced Concrete Design II
Sub-Frames Simplified
sub-frame >>> One point sub-frame:
Roof Second floor
A
B
C
D
E
First floor
Complete 2D Frame
A
B
Simplified sub-frame at point A
B
C
D
Simplified sub-frame at point C
BFC32803 Reinforced Concrete Design II
Type of Frame 1) Braced Framed (BF) Frames that not contribute to the overall stability of the structure. None of the lateral actions, including wind, are transmitted to the columns and beams but carries by bracing members such as shear wall. Support vertical actions only. BFC32803 Reinforced Concrete Design II
Type of Frame 2) Unbraced Framed (UBF) Frame that contribute to the overall stability of the structure. All lateral actions, including wind, are transmitted to the columns and beams since there are no bracing members such as shear wall are provided. Support vertical and lateral actions BFC32803 Reinforced Concrete Design II
Method of Analysis Primary
objective: to obtain a set of internal forces and moments throughout the structure that are in equilibrium with the design loads for the required loading combinations.
General
provisions to analysis are set out in EN 1992-1-1 Section 5.
Vertical load
Vertical load + Horizontal load
Load transfer from slabs to beams
Load transfer from slabs to beams ; wind to column
Design action patterns: maximumminimum Moment distribution method Fixed end moments, Shear forces, Bending moments
BFC32803 Reinforced Concrete Design II
General Consideration General
consideration for sub-frame analysis:
i)
Method of sub-frame analysis can be conducted using onelevel sub-frame, two-point sub-frame or one-point sub-frame with continuous beam.
ii)
The column or/and beam ends remote from the beam under consideration may generally be assumed to be fixed unless the assumption of pinned is clearly more reasonable.
iii) Stiffness for interior beam is KB. iv) Stiffness for fixed end (beam elements) posses half their actual stiffness, 0.5KB. v)
The arrangement of the design ultimate variable loads should be such as to cause the maximum moment the column. BFC32803 Reinforced Concrete Design II
Method of Analysis
One-level sub-frame Each sub-frame mat be taken to consist of the beams at one level together with the columns above and below.
KB1
KB2
KB3
At least four cases combination of actions: [Max][Min][Max]; [Min][Max][Min] [Max][Max][Min]; [Min][Max][Max] BFC32803 Reinforced Concrete Design II
Method of Analysis ii)
Two-point sub-frame The moments and forces in certain individual beam may be found by considering a simplified sub-frame consisting only of the beam, the columns attached to the end of that beam and the beams on either side is any.
KB1
0.5KB2
0.5KB1
KB2
0.5KB2
Load at interior beam where stiffness = KB is always for maximum design load. BFC32803 Reinforced Concrete Design II
Method of Analysis iii) One-point sub-frame with continuous beam The moments and forces in the beams at one level considering the beams as a continuous beam over supports providing no restraint to rotation. The ultimate moment for column distribution procedure 0.5KB1
0.5KB1
0.5KB2
BFC32803 Reinforced Concrete Design II
simple moment
0.5KB3
Combination of Actions Action
on buildings is due to permanent (dead load), variable (imposed, wind, dynamic, seismic loads) and accidental load.
Mostly
multistory buildings for office or residential purpose are design for dead, imposed and wind loads.
Separate
actions must be applied to the structure in appropriate directions and various types of actions combined with partial safety factors selected to cause the most severe design condition.
Maximum Minimum Wind
design load = 1.35Gk + 1.5Qk
design load = 1.35Gk
load = 1.2Wk
Vertical
load due to wind = 1.2Gk + 1.2Qk BFC32803 Reinforced Concrete Design II
Combination of Actions For
the combination of dead load and imposed load, the following loading patterns are considered: Braced frame
1) All spans loaded with maximum dead plus imposed loads 2) Alternate spans loaded with maximum dead load and imposed load and all other spans loaded with minimum dead load
Unbraced frame
1) Three cases loading arrangements as braced sub-frame 2) Vertical actions for sub-frame 3) Wind load for complete frame BFC32803 Reinforced Concrete Design II
Analysis of Braced Frame Procedure:
1. Analyse all actions, maximum and minimum design loads 2. Calculate moment inertia, I = bh3 /12 3. Calculate stiffness of beams and columns, k = I/L 4. Determine distribution factor, DF = ki / Σk 5. Determine fixed end moment (FEM) of beams 6. Perform moment distribution by cases: a) Case 1 [Max][Max][Min] b) Case 2 [Min][Min][Max] c) Case 3 [Max][Min][Max] d) Case 4 [Min][Max][Min] 7. Calculate actual shear force and bending moment 7. Draw BMD and SFD diagrams BFC32803 Reinforced Concrete Design II
Wind Loading Wind
forces are variable loads which act directly on the internal and external surfaces of structures.
The
intensity of wind load on a structure is related to the square of the wind velocity and the dimension of the members that are resisting the wind.
Wind
velocity is dependent on:
a)Geographical location b)The height of the structure c) The topography of the area d)The roughness of the surrounding terrain
BFC32803 Reinforced Concrete Design II
Wind Loading The
response of a structure to the variable action of wind can be separated into 2 components: Background component
Resonant component
- Involves static deflection of the structure under the wind pressure
- Involve dynamic vibration of the structure in response to changes in wind pressure - Relatively small and structural response to wind forces is usually treated using static method of analysis.
- Example: Natural wind
- Example: High-fluctuate wind, hurricane, micro-burst, windblast
BFC32803 Reinforced Concrete Design II
Wind Loading Wind
creates pressure of the windward side of a buildings and suction on three sides.
BFC32803 Reinforced Concrete Design II
Effect of Wind
Hurricane Sandy batters New York with howling winds
Building failure due to high pressure wind from Hurricane Katrina
BFC32803 Reinforced Concrete Design II
Wind Analysis Three
procedures are specified in MS 1553:2002, Malaysian Standard for the calculation of wind pressures in buildings: 1)
The simplified procedure: Limited in application to building of rectangular in plan and not greater than 15 m high
2)
The analytical procedure: Limited to regular buildings that are not more than 200 m high and structure with roof spans less than 100 m
3)
The wind tunnel procedure: Used for complex building BFC32803 Reinforced Concrete Design II
Wind Analysis Simplified
procedure (MS1553 Appendix A) p
0.613 Vs
2
2
M z ,cat C pe
C pi
where:
p V s
= The design wind pressure in Pa = The basic wind speed (Figure A1)
M z ,cat = The terrain/height multiplier (Table A1) C pe
= The external pressure coefficient for surface of enclose building ( A2.3 and A2.4)
C pi
= The internal pressure coefficient for surface of enclose building which shall be taken as +0.6 or -0.3. The two cases shall be considered to determinate the critical load requirements for the appropriate condition . BFC32803 Reinforced Concrete Design II
Wind Analysis Analytical
procedure(MS1553 Section 2) p
where: V des = Vsit l
l
Vsit
0.613 Vdes
2
CfigCdyn
= The design wind speed = Importance factor (Table 3.2)
Vs M d M z ,cat M s M h = Site wind speed
V s = Basic wind speed 33.5m/s for zone I and 32.5m/s for zone 2 (refer Figure 3.1)
M d = Wind directional multiplier = 1.0 M z ,cat = Terrain/height multiplier (Table 4.1) M s = Shielding multiplier (Table 4.3) equal to 1.0 if the effects of shielding are ignored or not applicable. BFC32803 Reinforced Concrete Design II
Wind Analysis M h = Hill shape multiplier. Shall be taken as 1.0 except that for particular cardinal direction in the local topographic zones.
Cfig
C peK a K c K 1K p = Aerodynamic shape factor for external pressure.
C pe = External pressure coefficient ( Table 5.2.a and 5.2.b) for windward and leeward walls respectively for rectangular enclosed building
K a K c K 1K p = Area reduction factor, combination factor, local pressure factor and porous cladding reduction factor respectively. All shall be taken as 1.0 in most cases.
C dyn = Dynamic response factor. Shall be taken as 1.0 unless the structure is wind sensitive. BFC32803 Reinforced Concrete Design II
Wind Analysis Wind
tunnel procedure
BFC32803 Reinforced Concrete Design II
Analysis of Unbraced Frame Procedure:
1. Calculate design wind load, Wd=1.2Wk 2. Calculate lateral point load at each level of frame a) Assume contraflexure point at center of frame b) Axial loads in column are in its proportion to distances from the centre of gravity of frame c) All columns are equal cross-section area 3. Lateral load analysis using Cantilever Method. - Calculate axial force in columns, then shear force in beams and columns from top to ground levels. 4. Vertical load analysis due to wind, 1.2 Gk + 1.2Qk - analysis of one level sub-frame BFC32803 Reinforced Concrete Design II
Analysis of Unbraced Frame 1.2W K A3
B3
C 3
D3
A2
B2
C 2
D2
A1
B1
C 1
D1
+
A3
B3
C 3
D3
Vertical
A2
B2
C 2
D2
1.2GK +1.2QK
1.2GK +1.2QK
B1
C 1
1.2W K 1.2W K 1.2W K
Lateral
load of wind load
load due to wind pressure
1.2GK +1.2QK A1
BFC32803 Reinforced Concrete Design II
D1
Tutorial 1) The framing plans for a multistory building are shown in the layout. Analyze sub frame 3/A-D, Level 1 to determine shear forces and bending moments of corresponding beams and columns. Use all the three methods of analysis. Given the following data: Permanent office building (Design life 50 years); Location: Near sub-urban (Zone 1 of Malaysia wind speed mapping), Topography: Flat area –slope
