155
Prob. 14.1
(a)
3
2
2
in. 7.82
6
)5.9(5.5
6
bh
Sx
(b)
(c) Refer to Example 14.16
2
)(
AdII
oy
——————————————————
Prob. 14.2
(a)
4
42
3
2
in. 8.1160
in. 5.712)079.3(40
12
)10(4
x
x
I
I
3
(top)
(top)
in. 236
921.4
8.1160
c
I
S
x
x
Ix = 5170 + 6090 = 11,260 in.4
—————————————————-
Prob. 14.3
W18x71: Sx = 127 in.3
)28)(071.040.0(
22
wL
156
14-2
Prob. 14.5 See Prob. 14.2(a)
———————————————–
Prob. 14.6 See Prob. 14.2(b)
ft–k 600
8
)40(3
8
22
wL
M
——————————————————
Prob. 14.7
Steel rod: 25 mm diam.
————————————————
Prob. 14.8
Square steel bar: 38 mm x 38 mm
mm 1015.9
6
)38(38
6
33
22
x
bh
S
—————————————————–
Prob. 14.9
A992: Fy = 50 ksi,
W36x302: Zx = 1280 in.3
(Consider only the strong axis)
MR = 0.6FyZx = 0.6(50)(1280) = 38,400 k-in.
= 3200 k-ft
Prob. 14.11
MPa 36.2
)1020(4
4
mm 1031.11
)120(7854.07854.0
3
23
22
V
f
dA
20(6
(b) 4 above and below the N.A.;
4
3
NA
in. 4000
12
)20(6
I
psi 84
)6(4000
)4( Ib
fv
8 above & below N.A.:
2
2
2
in. 12
in. 9
yaQ
a
y
157
14-3
Prob. 14.13
(a) W14x30:
A = 8.85 in.2
Ix = 291 in.4
flange
2
385.0
90.6)385.0(73.6Q
(b) ksi 57.11
)270.0(8.13
1.43
w
vdt
V
f
——————————————————
Prob. 14.14
W460x60: d = 455 mm
tw = 8.0 mm
Prob. 14.16
A = 0.7854(10)2
= 78.54 in.2
4
)10(
I
(a)
42
in. 6.122)875.1(12
3
(bott) in. 15.25
875.4
6.122
c
I
Sx
Fully plastified section (N.A. is at the bottom of the
top flange):
Zx = 8(1.5)(0.75) + 6(2)(3) = 45 in.3
158
Prob. 14.18 (Refer to Prob. 14.17)
L= 14 ft, Fy = 36 ksi
(a) My = FySx = 36(25.15)/12 = 75.5 k-ft
14
L
(b) My = FySx = 36(108.7)/12 = 326 k-ft
—————————————————–
Prob. 14.19
Prob. 14.20
4×12 (S4S) Hem-fir
A = 39.4 in.2
ft–lb 6046
8
8
M
(O.K.) psi 150 psi 76.7
psi 7.76
)4.39(2
)2015(3
2
3
2
2
A
V
f
v
—————————————————–
Prob. 14.21
ft –k 160
)64)(50(6.0
6.0
ft–k 6.152
4
)24(10
8
)24(286.1 2
ZFM
M
xyR
159
14-5
Prob. 14.22 Calculate all. load w (kN/m)
A992 W250x115
= 331×103 N·m
N/m10106
)10331(8
8
8
3
2
3
2
2
M
w
M
wL
R
R
kN/m 200
5
)501(2
2
2
L
V
w
V
wL
R
R
Therefore, all. load = 106 kN/m
—————————————————–
Prob. 14.23 (Refer to Example 14.13)
lb/ft 21.4
16
)3370(2
2
L
V
w
R
(a) All. total w = 123.4 lb/ft
Prob. 14.24
Calculate all. load w (lb/ft)
)7.79(2
2
k 7.79
)285.0)(98.13)(50(4.04.0
k/ft 8.25
5.6
22
V
dtFV
L
w
R
wyR
Prob. 14.25
Given: Fb =1600 psi, Fv= 100 psi
3×12 (S4S): A = 28.1 in.2
lb/ft 4.195 allowable
in. 72.11
25.1
65.14
in. 65.14
12
)5.2(25.11
12
3
4
33
w
c
I
S
bh
I
160
Prob. 14.29
(a)
(b)
42
3
1in. 5.458)154.6(12
12
)2(6
x
I
42
3
2in. 0.363)846.3(24
12
)2(12
x
I
42
3
3in. 6.106)154.1(16
12
)8(2
x
I
Total Ix = 928.1 in.4
(top)
—————————————————–
Prob. 14.30 (See Prob. 14.29(a))
psi 953
255
)12(250,20
ft–lb 250,20
8
2
x
bS
M
f
wL
M
—————————————————–
MPa 93.6N/m 1093.6
m 1013.82
m) 10m(75N 2600
26
46–
-3
I
Mc
fb
(b)
46
m 105.12
(a)
MPa 4.10
N/m 104.10
105.12
)1050(2600 26
6
3
I
Mc
fb
(b)
3
161
Prob. 14.33
——————————————————
Prob. 14.34
—————————————————–
Prob. 14.35
a1 = 4 in.2
a2 = 3 in.2
a = 7 in.2
in. 643.2
)5.1(3)5.3(4
ay
y
Prob. 14.36
W920x390 Fy = 345 MPa
Zx = 18,000×103 mm3
MR = 0.60FyZx
psi 840,15
91.9
)12(080,13
(max)
x
bS
M
f
—————————————————–
Prob. 14.38
162
14-8
Prob. 14.38 (cont.)
On plane x-x:
—————————————————–
Prob. 14.39
Rect. Beam: 100 mm x 250 mm
46
3
mm 102.130
)250(100
x
I
—————————————————–
Prob. 14.40 (See Prob. 14.29(a))
Ix = 1786.6 in.4, Vmax = 4500 lb
Max. fv occurs at N.A. (axis x-x):
Q1 = 10(2)(6) = 120 in.3
——————————————————
Prob. 14.41
3
42
3
1
)8(2
in. 1013)5(20
12
)2(10
2
x
I
Web: psi 4.103
)2(1098
)100(2270
Ib
VQ
fv
Flange: psi 7.20
)100(2270
v
f
Plane y-y; (neutral axis)
Qy(flng) = 5.675(0.940)(3.15)(2) = 33.61 in.3
ksi 511.0
)85.35(270
)36.35(140
v
f
Web-flange junction:
Qy = 5.675(0.940)(3.15)(2) = 33.61 in.3
)61.33(140
163
14-1
—————————————————–
Prob. 14.43 W10x45: L = 14 ft
Zx = 54.9 in.3, d = 10.10 in., tw = 0.350 in.
k/ft 60.5
14
)3.137(8
8
ft–k 3.137
12
)9.54)(50(6.0
(a)
22
total)( L
M
w
M
R
R
—————————————————–
Prob. 14.44
k 210
Qx(flng) =10. 5(0.760)(14.52) = 115.9 in.3
Qx(web) = 14.14(0.545)(7.07) = 54.5 in.3
Qx(total) = 170.4 in.3
in. 479.3
5625.055.3
)405.6(5625.0)015.3(55.3
A
Ay
y
Ix = 22.1 + 3.55(0.464)2 + 0.5625(2.926)2
= 27.68 in.4
164
14-2
Prob. 14.47
Mmax = 400(8)/4 = 800 lb-ft
Vmax = 400/2 = 200 lb
(a) Not glued:
(b) Glued:
psi 600
16
)12(800
in. 16
6
)4(6
6
3
22
x
b
x
S
M
f
bh
S
—————————————————–
Prob. 14.48
a1 = 4 in.2, a2 = 4 in.2, a = 8 in.2
in. 375.2
8
)25.0(4)5.4(4
y
Prob. 14.48 (cont.)
(Tension) psi 3710
55.57
)375.2)(12(7500
on)(Compressi psi 9580
55.57
)125.6)(12(7500
(bott)
(top)
b
b
f
I
Mc
f
Vmax = 10,000/2 = 5000 lb
psi 1630
)5.0(55.57
Ib
f
v
At web-flange junction:
Q = 8(0.5)(2.125) = 8.5 in.3
psi 1477
)5.0(55.57
)5.8(5000
(web)
v
f
2
33
22
mm 10125
6
)50(300
6
bh
Sx
mm 1071.2
5.1
)8)(10125(0.11
8
max
3
3
w
SF
Lxb
165
Prob. 14.50
Fv = 60 psi
4
3
in. 72
)6(4
x
I
72
I
—————————————————–
Prob. 14.51
Fv=1.5 MPa, Fb = 10 MPa
(more)
33
12
)250(200
12
)300(250
x
I
4
84
2
2
wL
wLPL
M
kN 25.45N 1045.25
2
)4(107.2
1013.182
2
2max
22
3
3
3
wL
VP
wLP
V
Smaller controls: P = 14.74 kN
—————————————————–
Prob. 14.52
166
14-4
Prob. 14.52 contd
a1 = 16 in.2
a2 = 12 in.2
a = 28 in.2
ay
y
Max. shear stress at the N.A.:
in. 94.27
2
)286.5(2
3
2
Q
————————————————————
Prob. 14.53
Vmax = 920 lb
a1 = 6 in.2
a2 = 6 in.2
42
3
1
in. 148)5.3(6
12
)1(6
2
x
I
Prob. 14.54
6×12 (S4S): wt. = 17.5 lb/ft
ft–lb 709
8
)18(5.17
ft–lb 150,18)121(
12
1800
2
wt.beam
M
SFM xbR
Allowable P = 2907 lb
—————————————————–
Prob. 14.55
6×18 (S4S): wt. = 26.7 lb/ft
ft–lb 1081
8
)18(7.26
2
wt.beam
M
Allowable M for superimposed loads:
42,150 1081 = 41,069 lb-ft
lb 6845
6
069,41
ft)6(
max PPM
)18(7.26
lb 8990
5.1
)3.96(140
5.1
AF
Vv
R
167
Prob. 14.56
top
2
3
2
3
)96.0(10
12
)10(1
)96.6(16
12
)2(8
in. 04.6
241016
)1(24)7(10)13(16
I
A
Ay
y
xx
N.A. is located 1 above the top of the bottom
flange (for equal areas).
Zx = 16(10) + 9(4.5) + 1(0.5) + 24(2)
= 249 in.3
Shape factor = Z/S = 249/187.3 = 1.33
—————————————————–
Prob. 14.57
L = 30 ft, Fy = 50 ksi
W18x50: Sx = 88.9 in.3, Zx = 101 in.3
NOTES
168