Table of Contents
Homework 12 (due June 28)

— David Wagner 2007/06/27 15:34

Problem 1.

Solve problem 10.3 in your textbook

“Using statics equations, determine the values of Pn and Mn for the column shownm, assuming it is strained to -0.00300 on the right-hand edge and to +0.00200 on its left-hand edge. f'c = 4000 psi, fy = 60,000 psi. (Ans. Pn = 608.9 k, Mn = 399.1 ft-k)”

c={{0.003}/{0.003+0.002}}*24=14.4 in 

   |--7.2"-|---10.8"---|
  |--9.6"--|----14.4"---|
  |-------- 24" --------|

epsilon prime_s = {{10.8}/{14.4}}*0.003=0.00225 > 0.002 ∴yields

espilon_s = {{7.2}/{9.6}}*0.002=0.0015

a=0.85c=0.85*14.4=12.24 in

C_c=0.85*12.24*14*4==-582.6 k

C prime_s=60*1.58-0.85*1.58*4=94.8-5.372=-89.4 k

T_s=0.0015*29000*1.58=+68.7 k

P_n = 89.4+582.6-68.7=603.3 k

Pn=603.3 k

M_n=582.62*(9+12-{12.24/2})+89.4*18-603.3*9=8669+1609-5430=4849 kip-in

Mn=404.1 kip-ft

Problem 2.

Solve problem 11.1 in your textbook

Assume Eg=Eb.

I_c=0.7*{bh^3}/{12} = 0.7*{12*16^3}/{12}=2867

{E I_c}/{l} = 2867/{12*12}=19.91E

I_g=0.35*{bh^3}/{12} = 0.35*{12*20^3}/{12}=2800

{E I_g}/{l} = 2800/{24*12}=9.722E

Psi_C =10

Psi_D ={2*19.91}/{1*9.722}=4.096

Psi_E ={1*19.91}/{1*9.722}=2.048

kCD=0.93
kDE=0.88

Problem 3.

Solve problem 11.4 in your textbook

Assume Eg=Eb.

I_c=0.7*{bh^3}/{12} = 0.7*{12*16^3}/{12}=2867

{E I_c}/{l} = 2867/{14*12}=17.07E

I_g=0.35*{bh^3}/{12} = 0.35*{12*20^3}/{12}=2800

{E I_g}/{l} = 2800/{28*12}=8.333E

Psi_A =10

Psi_B ={2*17.07}/{1*8.333}=4.098

Psi_C ={1*17.07}/{1*8.333}=2.048

kAB=2.44
kBC=1.80

Problem 4.

Redo problem 11.4 in your textbook but using f’c = 6000 for columns and f’c = 3000 psi for beams.

I_c=0.7*{bh^3}/{12} = 0.7*{12*16^3}/{12}=2867

{E I_c}/{l} = {6*2867}/{14*12}=19.91102.4

I_g=0.35*{bh^3}/{12} = 0.35*{12*20^3}/{12}=2800

{E I_g}/{l} = {3*2800}/{28*12}=9.72225.00

Psi_A =10

Psi_B ={2*102.4}/{1*25.00}=8.192

Psi_C ={1*102.4}/{1*25.00}=4.096

Unbraced.

kAB=2.83
kBC=2.38

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