a.) A simply supported uniformly loaded beam has a shear diagram as shown. What

Question

a.) A simply supported uniformly loaded beam has a shear diagram as shown. What is the uniform load on the beam and the bending moment at midspan? Picture above.

b.) A W14x53 and a W12x53 both have the same cross-sectional area. Which of these two shapes would probably be more effective as a beam? Explain your answer.

A. W14x53

B. W12x53

Thanks for your help. I will rate lifesaver :) Please don't tell me that you have it in your notebook and you'll send it in my inbox if I rate lifesaver. I won't rate if that's the case. I really need help with this problem and this shouldn't be a website just to get points out of.

Explanation / Answer

if uniform load

Ra=Rb
total load=Ra+Rb=2800
w=weight distribution
L=total length
w*L=2800
w=116.6667  (it is also the slope of shear diagram)

Moment= integrate from 0 to 12, wx dx   this is exactly the area of shear diagram

moment at middle=the area of the trangle

M=1400*12/2=8400 [ unit: force*length]  this is also the max moment

stress=Moment*C/I 

you want to have a smaller stress in the beam

so choose the smaller C/I value (C=d/2, I is I X-X)

W14x53: c=d/2=6.96, Ixx=541  C/I=0.12865

sorry I don't have data for W12x53, calculate C/I, then choose the smaller C/I

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.