STRC10 Masonry Part1 0716
March 23, 2017 | Author: Kevin | Category: N/A
Short Description
PPI2PASS SE Exam Review Course Fall 2016 Lecture 10 Structural Engineering Course...
Description
Structural Engineering Exam Review Course
Masonry (Part 1)
Design of Masonry Structures (Part 1) Structural Engineering Review Course
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
1
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Lesson Overview Masonry (Part 1) • Construction Details • ASD and SD Methods • Load Combinations • Masonry Beams in Flexure • Beams in Shear • Design of Masonry Columns • Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
2
2
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Learning Objectives You will learn • fundamentals of masonry design using ASD and SD • member design for flexure and shear • member design for combined flexure and compression • code requirements for detailing shear walls in seismic regions
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
3
3
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Prerequisite Knowledge You should already be familiar with • structural analysis • mechanics of materials
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
4
4
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Referenced Codes and Standards • Building Code Requirements and Specification for Masonry Structures (MSJC, 2011) • International Building Code (IBC, 2012) • Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7, 2010)
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
5
5
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Construction Details reinforcement and grout (MSJC Sec. 1.16, Specifications Sec. 3.4) • Rebar must be securely supported to prevent displacement during grouting. • Grout must comply with ASTM C476. • Grout is classified fine or coarse according to maximum aggregate size. • Type of grout must be selected per MSJC Table 1.20.1.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
6
6
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Construction Details grouting requirements (MSJC Specifications Sec. 3.5D) Grout may be placed in one continuous operation with a lift not exceeding 12.67 ft if • masonry has cured at least 4 hr • grout slump is between 10 in and 11 in • there are no intermediate bond beams
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
7
7
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
ASD and SD Methods design methods • both ASD and SD are acceptable, per MSJC Sec. 1.1.3 • exam permits either allowable stress design (ASD) • governed by MSJC Chap. 2 • traditional method to masonry design strength design (SD) is governed by MSCJ Chap. 3 STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
8
8
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Load Combinations – ASD Allowable Stresses allowable tensile stress in steel reinforcement (MSJC Sec. 2.3.3) 32,000 psi for grade 60 reinforcement 20,000 psi for grade 40 or grade 50 reinforcement compressive stress in masonry due to flexure (MSJC Sec. 2.3.4.2.2) 0.45 ′
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
9
9
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Load Combinations – ASD Allowable Stresses material properties • elastic modulus given by MSJC Sec. 1.8.2.2 • steel reinforcement, • concrete masonry,
29,000,000psi 900 ′ psi
• alternative method: Elastic modulus may be calculated from a compression prism test.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
10
10
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Load Combinations – SD Design Strength multiply nominal strength of member by = 0.90 for flexure, axial load, and combinations thereof = 0.80 for shear = 0.50 for anchor bolts, strength governed by masonry except for pullout = 0.90 for anchor bolts, strength governed by anchor bolt steel = 0.65 for anchor bolts, strength governed by anchor pullout = 0.60 for bearing on masonry surfaces
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
11
11
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure reinforcement requirements (MSJC Sec. 1.16, IBC Sec. 2107) • maximum bar size allowed is #11 (#9 for SD) • maximum db ≤ t /8 or 1/4 of the least dimension of the cell, course, or collar joint • Clear distance between parallel bars must not be less than db or 1 in.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
12
12
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Reinforcement in Beams Example 6.1
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
13
13
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Reinforcement in Beams Example 6.1
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
14
14
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Reinforcement in Beams
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
15
15
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Reinforcement in Beams
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
16
16
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure dimensional limitations (MSJC Sec. 1.13.1) • maximum permitted unbraced length, lc, is 120b 2 lc min 32b and d
• minimum bearing length is 4 in • minimum beam nominal depth, h, is 8 in • per MSJC Sec. 3.3.4.2.4, all beams must be solid grouted
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
17
17
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure development length and splice length of reinforcement • development length, ld, of reinforcement is ld
0.13db2 f y K f
' m
12 in
MSJC Eq. 2‐12, Eq. 3‐16
• K is the lesser of masonry cover, clear spacing of reinforcement or 9db. •
is 1.0 for no. 3 through no. 5, 1.3 for no. 6 through no. 7, and 1.5 for no. 8 and above.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
18
18
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure • The stress in the reinforcement due to an applied moment, M, is
• Fs = allowable stress in reinforcement • allowable tensile stress and the allowable compressive stress given by MSJC Sec. 2.3.2 as Fs = 20,000 lbf/in2 [for grade 40 or 50 reinforcement] Fs = 32,000 lbf/in2
[for grade 60 reinforcement]
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
19
19
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure development length and splice length of reinforcement • equivalent development length, le, of a standard hook in tension is (MSJC Sec. 2.1.7.5.1, Eq. 3‐15)
13
• lap splice length of straight reinforcing bars is found per IBC Sec. 2107.3 0.002db f s ld 12 in 40d b
• lap must be increased 50% for epoxy‐coating or at regions where fs ≥ 0.8Fs • welded or mechanical splices must develop 1.25fy
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
20
20
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Development Length Example 6.2
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
21
21
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Development Length Example 6.2
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
22
22
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Development Length
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
23
23
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Development Length
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
24
24
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure effective span length of masonry beams (MSJC Sec. 1.13.1)
Figure 6.1 Effective Span Length
• Span length, l, of a beam not built integrally with supports must be taken as clear span plus h, but need not exceed the distance between center of supports. • For a continuous beam, l is taken as the distance between center of supports.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
25
25
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure beams with tension reinforcement (ASD design procedure)
Figure 6.2 Elastic Design of Reinforced Masonry Beam
• The elastic design method is used to calculate compressive stress in masonry and tensile stress in reinforcement. • Service stresses are compared to allowable values.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
26
26
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure beams with tension reinforcement (ASD design procedure) • assume beam dimensions and masonry strength • assume j = 0.9
• calculate Mm and Ms • Mm and Ms must each exceed M • increase beam size, As or f′m if needed
• calculate As = M/Fsjd • select bar size and number required • calculate ρ and ρn • determine k and j
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
27
27
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
28
28
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure beams with tension reinforcement (ASD analysis procedure) • calculate ρ and ρn • determine k • calculate j
• compare fb to Fb; increase beam size or f′m if needed • compare to fs to Fs; increase reinforcement if needed
• calculate fb • calculate fs
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
29
29
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Poll: Masonry Beams in Flexure For a masonry beam being analyzed, fs ≤ Fs, but fb > Fb. Which of the following options would be effective when redesigning the beam? (I) increase the beam depth (II) increase the beam reinforcement (III) increase f′m (A) I only (B) II only (C) I and III only (D) I, II, and III
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
30
30
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Poll: Masonry Beams in Flexure For a masonry beam being analyzed, fs ≤ Fs, but fb > Fb. Which of the following options would be effective when redesigning the beam? (I) increase the beam depth (II) increase the beam reinforcement (III) increase f′m (A) I only (B) II only (C) I and III only (D) I, II, and III
Increasing the beam depth or increasing f′m will make the beam work by reducing fb or increasing Fb respectively. Since the problem is the compressive strength in the masonry, increasing the beam reinforcement will only slightly reduce the compressive stress. Changing beam depth or increasing the compressive strength will be a much more effective change. The answer is (C).
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
31
31
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure beams with tension reinforcement (SD procedure) • The design strength of a beam is computed and compared to factored loads. • The strain distribution at design strength is assumed to be linear. • The compressive strain of masonry in compression is 0.0025. • Tension reinforcement stress is equal to yield.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
32
32
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure minimum reinforcement area (MSJC Sec. 3.3.4.2.2.2) • Flexural strength must not be less than 1.3 times the cracking moment, Mcr.. • The modulus of rupture, fr, is given by MSJC Table 3.1.8.2. • Mn ≥ 1.3Mcr • Mcr = frSn
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
33
33
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Minimum Reinforcement Area Example 6.3
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
34
34
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Minimum Reinforcement Area Example 6.3
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
35
35
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Minimum Reinforcement Area
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
36
36
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Minimum Reinforcement Area
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
37
37
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure maximum reinforcement ratio (MSJC Sec. 3.3.3.5.1) • produces εm = 0.0025 (CMU), εm = 0.0035 (clay), and εs = 1.5εy
Figure 6.4 Maximum Reinforcement in Concrete Masonry Beams
• intended to ensure ductility at failure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
38
38
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure maximum reinforcement ratio (MSJC Sec. 3.3.3.5.1) • for grade 60 reinforcement, cmax
amax
m d 1.5 y m
0.0025 d 0.0025 (1.5)(0.00207) 0.446d 0.8cmax 0.357 d
• maximum reinforcement area, As,max, is max
0.286 f m' bd fy
• maximum reinforcement ratio, ρmax, is As ,max
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
As ,max
0.8amax bf m' 0.286bdf m' fy fy
39
39
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Maximum Reinforcement Ratio Example 6.4
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
40
40
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Maximum Reinforcement Ratio Example 6.4
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
41
41
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure SD design procedure • assume beam dimensions and masonry strength • calculate Ku Ku
Mu bd 2
• check maximum reinforcement requirements are met • check minimum reinforcement requirements are met
• calculate ρ Ku 1 1 ' 0.36 f m ' 0.80 f m fy
• select bar size and number required
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
42
42
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure SD analysis procedure • calculate stress block depth, a a
As f y 0.80bf m'
• calculate nominal strength, Mn a M n As f y d 2
• calculate design strength, Mn
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
43
43
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure The 12 in solid‐grouted concrete block masonry beam shown is simply supported over an effective span of 18 ft. The masonry has a compressive strength 2500 psi, and a modulus of elasticity of 2,250,000 psi. Reinforcement consists of four no. 7 grade 60 bars. The effective depth is 29 in, the overall depth is 32 in, and the beam is laterally braced at both ends. The self weight of the beam is 124 psf. Determine whether or not the beam is adequate for flexure.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
44
44
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure At midspan, the bending moment produced by the concentrated load, Mc, is
The beam self‐weight, w, is lbf w 124 2 (2.67 ft) 331 lbf/ft ft
At midspan, the bending moment produced by this self‐weight, Ms, is lbf 331 (18 ft) 2 2 wl ft Ms 8 lbf (8) 1000 kip 13.4 ft-kips
Ms
Wl (25 kips)(18 ft) 112.5 ft-kips 4 4
ASD Method At midspan, the total ASD moment is given by IBC load combination (16‐9) as M y M s M c 13.4 ft-kips 112.5 ft-kips 125.9 ft-kips
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
45
45
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure The allowable stresses, in accordance with MSJC Sec. 2.3.2, Sec. 2.3.3, and Sec. 2.3.4.2.2, are lbf E in 2 n s lbf Em 2,250,000 2 in 12.9
lbf Fb 0.45 f (0.45) 2500 2 in 1125 psi
29,000,000
' m
Fs 32,000 psi in (18 ft) 12 le ft b 11.63 in 18.6 32 [satisfies MSJC Sec. 1.13.1.2]
As 1.20 in 2 bd (11.63 in)(29 in) 0.00356 n (0.00356)(12.9) 0.0459
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
46
46
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure k 2 n ( n) 2 n (2)(0.0459) (0.0459) 2 0.0459 0.260
47,500 psi Fs [not satisfactory]
k 0.913 3 2M y
j 1 fb
in lbf (125.9 ft-kips) 12 1000 My ft kip fs (0.913)(29 in)(1.20 in 2 ) jdAs
The beam is not adequate. The beam depth and/or reinforcement should be increased to reduce the stresses.
jkbd 2
in lbf (2)(125.9 ft-kips) 12 1000 ft kip (0.913)(0.260)(11.63 in)(29 in) 2 1300 psi Fb [not satisfactory] STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
47
47
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure SD Method The total factored moment at midspan, Mu, is given by IBC load combination (16‐2) as M u 1.2 M s 1.6 M c (1.2)(13.4 ft-kips) (1.6)(112.5 ft-kips) 196.1 ft-kips
The stress block depth, a, is kips (1.20 in 2 ) 60 As Fy in 2 a kips 0.80bf m' (0.80)(11.63 in) 2.5 in 2 3.10 in
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
48
48
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Masonry Beams in Flexure SD Method The nominal strength, Mn, is
The design strength, Mn, is
a M n As Fy d 2 kips 3.10 in (1.20 in 2 ) 60 29 in 2 in 2 in 12 ft 164.7 ft-kips
M n (0.9)(164.7 ft-kips) 148.2 ft-kips M u [not satisfactory]
The beam is not adequate. The beam depth and reinforcement should be increased to increase the design strength.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
49
49
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Masonry Beams in Flexure biaxial bending • ASD method: determine combined stresses by calculating stress due to each moment independently and using superposition.
• SD method: the interaction equation is the most convenient way of determining adequacy of member.
• Sum of stresses should not exceed allowable stresses.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
50
50
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending Example 6.6
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
51
51
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
52
52
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
53
53
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
54
54
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
55
55
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
56
56
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
57
57
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
58
58
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
59
59
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Biaxial Bending
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
60
60
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Beams in Shear shear reinforcement (MSJC Sec. 2.3.6.4 and Sec. 3.3.4.2.3)
Figure 6.4 Shear Reinforcement
• reinforcement is a single bar with a hook at each end, hooked around longitudinal reinforcement • first bar placed within dv/4 • spacing of shear reinforcing bars is d ≤ h/2 ≤ 48 in • design shear calculated at d/2 from the support.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
61
61
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Beams in Shear design for shear – ASD method (MSJC Sec. 2.3.6.1.1) • area of shear reinforcement required is derived from
• shear stress in masonry, fv v fv bd
AFd Fvs 0.5 v s An s
• allowable masonry shear stress, Fvm P • 1 M ' Fvm 4.0 1.75 f m 0.25 An 2 Vd
• if fv > Fvm, shear reinforcement must carry residual stress
allowable shear stress, Fv Fv Fvm Fvs
• for a typical beam, Fv 2 f m'
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
62
62
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Beams in Shear design for shear – SD method • nominal masonry shear strength, Vnm Vnm
M 4.0 1.75 u Vu d v
Anv
f
• nominal shear strength, Vn = Vnm + Vns • for a typical beam, Vn 4 Anv f m'
' m
P 0.25 An
• area of shear reinforcement required is derived from A Vns (0.5) v s
f y dv
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
63
63
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Beams in Shear The 12 in solid‐grouted concrete block masonry beam shown is simply supported over an effective span of 18 ft. The masonry has a compressive strength 2500 psi. No shear reinforcement is provided. The effective depth is 29 in, the overall depth is 32 in, and the beam is laterally braced at both ends. The self weight of the beam is 124 psf. Determine whether or not the beam is adequate for shear.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
64
64
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Beams in Shear The beam self‐weight, w, is
At a distance of d/2 from the support, the shear produced by the concentrated load, Vc, is
lbf w 124 (2.67 ft) ft 331 lbf/ft
At a distance of d/2 from the support, the shear produced by the self‐weight, Vs, is lbf 331 18 ft 2.42 ft w( l d ) ft Vs 2 lbf (2) 1000 kip 2.6 kips
Vc
W 2.5 kips 12.5 kips 2 2
ASD Method The total ASD shear, V, is given by IBC load combination (16‐9) as V Vs Vc 2.6 kips 12.5 kips 15.1 kips
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
65
65
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Beams in Shear The allowable shear stress, Fv, in accordance with MSJC Eq. 2‐27, is limited to 2 f m' 2 2500
lbf 100 psi in 2
The shear stress, fv, as given by MSJC Eq. 2‐24, is fv
V bd
15,100 lbf (11.63 in)(29 in) 45 psi Fv [satisfies MSJC Sec. 2.3.6.1.2]
Per MSJC Sec. 2.3.6.1.2, M/Vd may be taken equal to 1.0. From MSJC Eq. 2‐2, the allowable shear stress in a beam without shear reinforcement, Fvm, is P 1 M ' Fvm 4.0 (1.75) f m (0.25) 2 Vd An 1 lbf 4.0 (1.75)(1.0) 2500 2 0 2 in 56 psi f v [satisfactory]
The beam is adequate for shear without shear reinforcement.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
66
66
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Beams in Shear SD Method The total factored shear, Vu, at a distance of d/2 from the support is given by IBC load combination (16‐2) as Vu 1.2Vs 1.6Vc (1.2)(2.6 kips) (1.6)(12.5 kips) 23.1 kips
The maximum nominal shear capacity permitted, Vn, assuming Mu/Vudv = 1.0, is limited by MSJC Eq. 2‐33 to lbf 2500 in 2 Vn 4 Anv f m' (4)(11.63 in)(29 in) 1000 lbf kip 67.5 kips
The maximum design shear capacity permitted, Vn, is Vn (0.8)(67.5 kips) 54.0 kips Vu [satisfactory] STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
67
67
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Beams in Shear The nominal capacity of the beam without shear reinforcement, Vnm, is given by MSJC Eq. 3‐23 as Vnm
M ' 4.0 (1.75) Anv f m 0.25Pu Vd 4.0 (1.75)(1.0) (11.63 in)
The design strength of the beam, Vnm, is Vnm (0.8)(37.9 kips) 30.4 kips Vu [satisfactory]
The beam is adequate for shear without shear reinforcement.
lbf 2500 2 in 0 29 in 1000 lbf kip 37.9 kips
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
68
68
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns dimensional limitations (MSJC Sec. 1.6, Sec. 1.14.1, and Sec. 2.3.4.3) • minimum column width is 8 in • distance between lateral supports is limited to 99r
• longitudinal reinforcement area is limited to (0.25% – 4%)An • at least 4 bars must be provided
• dmax ≤ 3t (nominal) • h ≥ 4t
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
69
69
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns Figure 6.6 Column Dimensions
dimensional limitations (MSJC Sec. 1.6, Sec. 1.14.1, and Sec. 2.3.4.3) • minimum tie diameter is ¼ in • tie spacing, s, must be least of 16 × longitudinal bar diameter, 48 × lateral bar diameter, or least column dimension • first and last ties must be within 0.5s from footing, slab, or beam horizontal reinforcement STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
70
70
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Column Dimensional Limitations Example 6.8
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
71
71
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Column Dimensional Limitations Example 6.8
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
72
72
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns axial compression in columns – ASD method (MSJC Sec. 2.3.4.2.1 and Sec. 2.3.4.3) • If h/r ≤ 99, the allowable axial load is h 2 Pa 0.25 f An 0.65 Ast Fs 1 140r ' m
• columns must be also be designed for eccentricity (min. 0.1t) • for grade 60 rebar, Fs = 32,000 psi
MSJC Eq. 2‐21
• If h/r > 99, the allowable axial load is 70r Pa 0.25 f An 0.65 Ast Fs h
2
' m
MSJC Eq. 2‐22
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
73
73
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns axial compression in columns: SD method (MSJC Sec. 3.2.4.1.1) • If h/r ≤ 99, the allowable axial load is given by MSJC Eq. 3‐18. Pn (0.80) 0.80 f m' ( An Ast ) Ast f y h 2 1 140r
• If h/r > 99, the allowable axial load is 70r Pn (0.80) 0.80 f ( An Ast ) Ast f y h
MSJC Eq. 3‐19 MSJC Eq. 3‐18
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
2
' m
74
74
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns Example 6.9
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
75
75
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
76
76
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
77
77
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
78
78
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
79
79
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Axial Compression in Columns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
80
80
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns combined compression and flexure: ASD method (MSJC Sec. 2.3.4.2.2) • Allowable compressive stress due to combined load is Fb 0.45 f m'
• When there is no tensile stress due to combined load, consider the section uncracked.
• Allowable compressive strength due to • Otherwise, section is cracked and axial load is per previous section. iterative approach is required.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
81
81
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns Figure 6.7 Uncracked Section Properties
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
Figure 6.8 Cracked Section Properties
82
82
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns combined compression and flexure SD method (MSJC Sec. 3.1.2 and Sec. 3.2.2) • Assume a neutral axis, C. • Equate compressive and tensile forces acting on section such that Pn Cm Cs T 0.64cbf m' As' s' As f y
• Adjust the neutral axis depth until force equilibrium is achieved. • The nominal moment strength, Mn, is b b a b M n Cm C s d ' T d 2 2 2 2
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
83
83
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure Example 6.10
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
84
84
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
85
85
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
86
86
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
87
87
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
88
88
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
89
89
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
90
90
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Combined Compression and Flexure
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
91
91
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Masonry Columns maximum reinforcement ratio for columns (MSJC Sec. 3.3.3.5.1) • similar to requirements for flexural members • axial loads are included in the analysis with P D 0.75 L 0.525QE
• maximum area of tension reinforcement, Amax, is Amax
0.286bdf m' P f y f s'
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
92
92
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Maximum Reinforcement Ratio Example 6.11
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
93
93
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Maximum Reinforcement Ratio
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
94
94
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Maximum Reinforcement Ratio
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
95
95
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls shear wall types (MSJC Sec. 1.6 and Sec. 1.18.3.2.3.1) ordinary plain • may be used only in seismic design categories A and B detailed plain • minimum no. 4 at 120 in vertical and horizontal • may be used only in seismic design categories A and B
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
96
96
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls shear wall types (MSJC Sec. 1.6 and Sec. 1.18.3.2.3.1) ordinary reinforced • minimum reinforcement per above and stress in reinforcement considered • may be used only in seismic design categories A, B, and C (up to 160 ft) intermediate reinforced • minimum reinforcement with reduced vertical bar spacing (48 in) • may be used only in seismic design categories A, B, and C
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
97
97
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls shear wall types (MSJC Sec. 1.6 and Sec. 1.18.3.2.3.1) special reinforced • minimum reinforcement per MSJC Sec. 1.18.3.2.6 designed to resist lateral forces • must be used in seismic design categories D, E, and F
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
98
98
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Poll: Shear Walls A two‐story masonry building is designed in seismic design category C. Which acceptable shear wall type includes the fewest detailing requirements? (A) ordinary plain (B) detailed plain (C) ordinary reinforced (D) intermediate reinforced (E) special reinforced
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
99
99
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Poll: Shear Walls A two‐story masonry building is designed in seismic design category C. Which acceptable shear wall type includes the fewest detailing requirements? (A) ordinary plain (B) detailed plain (C) ordinary reinforced
Since the building is seismic design category C, plain walls are not acceptable, so (A) and (B) are incorrect. Ordinary reinforced walls have fewer detailing requirements than intermediate or special reinforced walls, so (D) and (E) are incorrect. The answer is (C).
(D) intermediate reinforced (E) special reinforced
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
100
100
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls special reinforced shear wall requirements (MSJC Sec. 1.18.3.2.6) • ASD method: must resist 1.5 times the seismic forces • SD method: must resist shear corresponding to 1.25 times nominal flexural strength, except Vn need not exceed 2.5Vu • Shear reinforcement may be anchored around vertical reinforcement with a standard hook.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
101
101
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls Figure 6.11 Reinforcement Details for Special Reinforced Shear Wall Laid in Running Bond
Figure 6.12 Reinforcement Details for Stack Bond Special Reinforced Shear Wall
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
102
102
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls design for shear – ASD method V bd
fv • Shear stress in masonry, fv, is .
• Allowable masonry shear stress, Fvm, is 1 P M ' Fvm 4.0 1.75 f m 0.25 2 An Vd
• For special reinforced shear wall, decrease coefficient from ½ to ¼.
• Area of shear reinforcement required is derived from AFd Fvs 0.5 v s An s
• allowable shear stress, Fv = Fvm + Fvs • if M/Vd ≤ 0.25, Fv 3 f m' • if M/Vd ≥ 1.0, Fv 2 f m'
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
103
103
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls design for shear – SD method • nominal masonry shear strength Vnm
M 4.0 1.75 u Vu d v
Anv
P f 0.25 An ' m
• if Mu/Vudv ≤ 0.25, Vn 6 Anv f m' • if Mu/Vudv ≥ 1.0, Vn 4 Anv f m'
• area of shear reinforcement required derived from A Vns (0.5) v s
f y dv
• nominal shear strength, Vn = Vnm + Vns
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
104
104
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls design for flexure – ASD method • If flexural reinforcement is concentrated at ends and axial loads are light, design like a beam. Otherwise, use basic principles.
• Maximum flexural reinforcement for SRMSW with M/Vd ≥ 1.0 and with P > 0.05f′mAn is given by MSJC Sec. 2.3.4.4 as
• Compressive resistance of steel reinforcement is neglected unless lateral tie reinforcement is provided.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
105
105
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Design of Shear Walls design for flexure – SD method • If flexural reinforcement is concentrated at ends and axial loads are light, design like a beam. Otherwise, use basic principles.
• Maximum reinforcement is given by MSJC Sec. 3.3.3.5.1 through Sec. 3.3.3.5.4, based on M/Vd and the response modification factor, R.
• MSJC Sec. 3.3.4.2.2.2 requires Mn ≥ 1.3Mcr
• Maximum reinforcement may be waived if special boundary elements are provided.
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
106
106
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls Example 6.12
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
107
107
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
108
108
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
109
109
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
110
110
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
111
111
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
112
112
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
113
113
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Example: Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
114
114
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Learning Objectives You have learned • fundamentals of masonry design using ASD and SD • member design for flexure and shear • member design for combined flexure and compression • code requirements for detailing shear walls in seismic regions
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
115
115
Structural Engineering Exam Review Course
Masonry (Part 1)
Masonry (Part 1)
Lesson Overview Masonry (Part 1) • Construction Details • ASD and SD Methods • Load Combinations • Masonry Beams in Flexure • Beams in Shear • Design of Masonry Columns • Design of Shear Walls
STRC ©2015 Professional Publications, Inc.
© 2015 Professional Publications, Inc.
116
116
View more...
Comments