7/28/2019 CE 156 - HW 3
1/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
CE 156 - Homework 3
Prof. Ulpiano Ignacio
LRFD:
Pu = 1.2*(50kips) + 1.6*(135kips)
= kips
(KL)x = ft
(KL)y = ft
(a) A992
Fy = ksi Fu = ksi E = ksi
*choose sections in the AISC is such that local buckling will not occur, Q=1.0
=
W8x40
(kL/r)x =
7/28/2019 CE 156 - HW 3
2/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
(a) A572 Grade 60
Fy = ksi Fu = ksi E = ksi
*sections in the AISC is such that local buckling will not occur, Q=1.0
=
W8x40
(kL/r)x =
7/28/2019 CE 156 - HW 3
3/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
LRFD:
Pu = (90kips) + (320kips)
= kips
(KL)x = ft
(KL)y = ft
7/28/2019 CE 156 - HW 3
4/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
(b) *the first two trials passed it with a value of near 410 kips
Fy = ksi E = ksi
*choose sections in the AISC is such that local buckling will not occur, Q=1.0
=
W12x53
(kL/r)x =
7/28/2019 CE 156 - HW 3
5/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
LRFD:
Pu = 1.2*(300kips) + 1.6*(500kips)
= kips
(KL)x = ft
(KL)y = ft
7/28/2019 CE 156 - HW 3
6/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
For Fcr > 2Fy
Ie/I = [(b/2)^3]/[b^] = Fcr = [^2*Et*(1/8)]/[(kL/r)]1/8
43.8044885 16.5
46.5850468 16
50 15.4439451
32.1828895 77
33.3333333 75.6595701
33.3333333 18.9148925
16.666667 106.998789
19.0812352 100
21.1426429 95
3.92618008 270
4.96907166 240
6.49021605 210
50 0
36.8079382 18
38.9412963 17.5
34.8452067 18.5
26.4100141 85
29.81443 80
23.5570805 90
12.7208235 150
16.666667 131.046218
8.83390517 180
Fcr (ksi) kL/r
3.18020586 300
0
10
20
30
40
50
60
0 50 100 150 200 250 300
Fcr(ksi)
kL/r ratio
7/28/2019 CE 156 - HW 3
7/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
(b) LRFD:
Fy = ksi E = ksi Pu = 1.2*(65kips) + 1.6*(150kips)
*choose sections in the AISC is such = kips
that local buckling will not occur, Q=1.0
(KL)x = ft
*Use LRFD (KL)y = ft
7/28/2019 CE 156 - HW 3
8/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
for Fcr < 0.6Fy for Fcr >= 0.6Fy
Fcr = [^2*E]/[(kL/r)^2] Fcr has linear relation ship with kL/r until yielding
LRFD:
Pu = 1.2*(300kips) + 1.6*(500kips)
= kips
(KL)x = ft
(KL)y = ft
7/28/2019 CE 156 - HW 3
9/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
LRFD:
Pu = 1.2*(300kips) + 1.6*(900kips)
= kips
*Assume design beam is W14x145
A572, Grade 50: Fy = 50 ksi
Analysis on the plane of the frame
GA =
7/28/2019 CE 156 - HW 3
10/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
*Analysis on the plane perendicular to the frame
GA = r (128/sqrt(65))
> , yes Qs => (175/sqrt(65))
> , no Qs =
b/t (4.02/.595) > r (95/sqrt(65))
> ,no
21.7061 0.73651
6.7563 11.7833
216 211
20.2941 15.8764
253 250
285 318
65
193.846
252
10
10
50 65 29000
0.96
39.3366 184.971
113.432 44.6513
2753
10
35.8333
3.34259
10.72
7/28/2019 CE 156 - HW 3
11/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
(kL/r)x = (175/sqrt(50))
> ,no
d/t (14/.25) > (253/sqrt(50)) f = ksi
> ,yes *Fcr with Q=1.0
dE/t = = Qa = (dE/t)/(d/t) =
Q = QaQs =
=
= ksi
= 0.9*Fcr*Ag = 0.9*(26.0186ksi)*(13.5in^2) = kips
0.64572
26.0186
316
45.211 0.80734
141.16
20 13.435
24.7487
0.79982
56 35.7796
62.6122
35.7941
4.79985
2.48479
17.5005
67.6113
29000
7
83.3516
311.021
13.5
81.6327 42.9507
39.7351
30.7158
264
14
62.8272
29.5707
188
63.8298 70.2507
7/28/2019 CE 156 - HW 3
12/12
Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012
Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips
kips
kips
(b) Fy = 60 ksi
b/t (5/0.25) > (95/sqrt(60))
> ,yes Qs = =
> (175/sqrt(60))
> ,no
d/t (14/.25) > (253/sqrt(60)) f = ksi
> ,yes *Fcr with Q=1.0
dE/t = = Qa = (dE/t)/(d/t) =
Q = QaQs =
=
= ksi
= 0.9*Fcr*Ag = 0.9*(27.2611ksi)*(13.5in^2) = kips
Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips
kips
kips
(b) Fy = ksi
b/t (5/0.25) > (95/sqrt(100))
> ,yes Qs = => (175/sqrt(100))
> ,yes
d/t (14/.25) > (253/sqrt(100)) f = ksi
> ,yes *Fcr with Q=1.0
dE/t = = Qa = (dE/t)/(d/t) =
Q = QaQs =
=
= ksi
= 0.9*Fcr*Ag = 0.9*(27.2634ksi)*(13.5in^2) = kips
Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips
kips
kips
Live Load 158.918919
Dead Load 68.1081081
100
0.34894
192.027
27.634
336
2.11429 336
0.5
17.5
51.2487
56 25.3
39.0808 0.69787
Live Load 156.554054
Dead Load 67.0945946
20 9.5
0.57137
150.064
27.2611
331
2.11429 331
0.7411
22.5924
40.1755
56 32.6622
43.1748 0.77098
Dead Load
149.459459
64.0540541
20 12.2644
2.11429 316
Live Load