PE exam question - camber

[samiha]

Can anyone help me solve this problem? I’ve been trying to figure it out for a while and still haven’t gotten the answer right. The correct answer is (B). It seems like it should be a simple plug and chug but I guess it isn’t.

 

[biffnater]

Not sure if my approach is exactly correct... but I got answer B...

When you stretch those Bars    715K <----BEAM----> 715K    an upward force develops at the low point of the reinforcing( @ 5-inches)  ...

Using trig to firgure out upward force (triangle):   atan(20/(45x12)) = 2.12 degrees  , 715*tan(2.12) = 26.45 kips , force is at both ends, so upward force is twice this. Total Upward force = 53kips

deflection due to upward force = PL^3/(48EI) = 53*(90*12)^3/(48*4000*250000) = 1.39" upward.

Deflection due to self weight = 5*w*L^4/(384EI) = 5*(.8/12)*(90*12)^4/(384*4000*250000) = 1.18" downward

total deflection= 1.39" - 1.08" = 0.21" Upward

 

[samiha]

Thanks for sharing your approach! The problem makes sense now!