Please show steps and explain. I will rate. Thanks Problem 2: A beam with L-24ft
ID: 1712363 • Letter: P
Question
Please show steps and explain. I will rate. Thanks
Problem 2: A beam with L-24ft has a service live load P applied at midspan. The beam is a W14x68. Calculate the strength (oMn) and the maximum applied load P that can be applied given the following: a) Continuous lateral support b) Braced at the ends (calculate Cb and show your work -do not use tables) c) Braced at ends and midspan (calculate Cb and show your work - do not use tables) d) Compare the results from parts (a) to (c) and discuss the effect of lateral support conditions.Explanation / Answer
Span of beam = 24 ft
beam section = w14x68
factored moment at midspan due to self weight of beam = 1.2*0.068*242/8=5.86 kip-ft
a) When there is continuous lateral bracing,beam moment capapcity will be equal to plastic moment capacity
=431 kip-ft
Maximum allowable factored moment due to live load = 431-5.86=425.14 kip-ft
Maximum service level moment due to live load = 425.14/1.6=265.7 kip-ft
Moment due to Point load = P*24/4=6P
6P=265.7
P=265.7/6=44.28 kips
b) unbraced length = L=24 ft
Mp=431 kip-ft
Mr=270 kip-ft
Lp=8.69 ft
Lr=29.3 ft
Lp<L<Lr
capapcity of beam without Cb = 431-[(431-270)/(29.3-8.69)]*(24-8.69) = 311.4 kip-ft
For point load at midspan,
Mmax=PL/4
MA=PL/8
MB=PL/4
MC=PL/8
Cb = (12.5*PL/4)/[(2.5*PL/4)+(3*PL/8)+(4*Pl/4)+(3PL/8)]=1.32
moment capapcity of beam = 1.32*311.4=411 kip-ft
maximum allowable factored moment in beam due to live load = 411-5.86=405.14kip-ft
Maximum service level moment due to live load = 405.14/1.6=253.2 kip-ft
Moment due to Point load = P*24/4=6P
6P=253.2
P=253.2/6=42.2kips
c)unbraced length of beam = 12 ft
capacity of beam without Cb =431-[(431-270)/(29.3-8.69)]*(12-8.69)=405.1kip-ft
For the unbraced segment of beam,due to point load,
Mmax=PL/4
MA = PL/16
MB=PL/8
MC=3PL/16
Cb = (12.5*PL/4)/[(2.5*PL/4)+(3*PL/16)+(4Pl/8)+(3*3PL/16)]=1.67
Moment capapcity of beam with Cb=1.67*405.1=676.52 kip-ft.
However, the beam capapcity cannot exceed its plastic moment capapcity.Therefore ,moment capacity of beam=431 kip-ft
Maximum allowable factored moment due to live load = 431-5.86=425.14 kip-ft
Maximum service level moment due to live load = 425.14/1.6=265.7 kip-ft
Moment due to Point load = P*24/4=6P
6P=265.7
P=265.7/6=44.28 kips
c) As we can see that in part (a),due to presence of continuous bracing, the entire plastic moment capapcity of beam is developed. this means full utilisation of material can be done .
In part (b), the moment capapcity of beam was not fully utilised because of unbraced length of 24 ft.This results in partial utilisation of material strength.
in part (c), the moment cpapcity increased drastically compared to part (b) by just providing brace point at midpsan.This resulted,with the help of Cb, in full utilisation of material because the beam plastic momenmt capapcity could be developed.
Therefore, the capapcity of beams can be enhanced by providing brace points,which otherwise would result in providing uneconomical and hight tonnage steel beams