Problem: Utilizing the ACI code load combinations discussed in class, determine

Question

Problem: Utilizing the ACI code load combinations discussed in class, determine the Ultimate Moment, Mw, for the following members at the section A-A (in all cases, A-A refers to the midspan, or the support). Where more than one load equation is needed, present results for each load equation and identify the controlling equation. In all cases, the density of concrete may be taken as 150 pef to calculate D. Only the ultimate moment at section A-A is to be calculated (i.e. you do not need to draw shear/moment diagrams, however, show the steps for all your calculations). L=4.75kipft A-A L-2.5kip/ft 20" long 3.5' high 2" wide (refers to dimension into page) A-A 6 (between supports) 24" high 18" wide L-3ki A-A L-3.25kip/ft L-110kips 4 long 21" high 15" wide W-2kip/ft W-1.5kip/ft E-3.25kip/ft 22 long (beam centerline length) 21" high 18" wide 20 tal (column centerline height) 36" high 18" wide 27.5' tall 4.5 high 4.5' wide Assume that distributed loads in problem 4 are applied to centerline A-A A-A

Explanation / Answer

1)depth of beam =3.5 ft

width of beam=2 ft

unit weight of concrete=150 pcf

self weight of beam = 3.5*2*150/1000=1.05 kip/ft

beam span=20 ft

moment at A-A due to dead load = 1.05*202/2=210 kip-ft

moment at A-A due to live load = 0.5*20*4.75*2*20/3=633.33 kip-ft

factored moment at A-A per load combination 1.2D+1.6L =Mu= (1.2*210)+(1.6*633.33)=1265.33 kip-ft

2)beam depth = 24"=2 ft

beam width=18"=1.5 ft

self weight of beam = 1.5*2*150/1000=0.45 kip/ft

reaction at each support due to dead load = 0.45*(4+6+4)/2=3.15 kips

moment at A-A due to dead load = 3.15*3 - 0.45*7*3.5=-1.575 kip-ft=1.575 kip-ft(tension on top side)

reaction at each suport due to live load = 2.5*(4+6+4)/2=17.5 kips

moment at A-A due to live load = 17.5*3 - 2.5*7*3.5=-8.75 kip-ft=8.75 kip-ft(tension on top side)

factored moment at A-A per load combination 1.2D+1.6L = (1.2*1.575)+(1.6*8.75)=15.89 kip-ft(tension top side)

3)depth of beam = 21 " = 1.75 ft

width of beam=15"=1.25 ft

self weight of beam = 1.75*1.25*150/1000=0.328 kip/ft

moment at A-A due to dead load = 0.328*142/8=8.04 kip-ft

moment at A-A due to live load = 3*142/8=73.5 kip-ft

factored moment at A-A due to load combination 1.2D+1.6L = (1.2*8.04)+(1.6*73.5)=127.25 kip-ft

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