Pretty stuck on a beam bending question.. so the questions asks to calculate the

Question

Pretty stuck on a beam bending question.. so the questions asks to calculate the max end load on a cantilever beam if the stress is to not exceed 350MN/m, it is a hollow rectangular beam with dimesions 100x50x5 with the 100mm height being vertical. i have calculated the I value using I=BH^3/12 - bh^3/12 and have then calcualted M to be 12.1x10^3, from rearranging F=MY/I to M=FI/Y. so my question is what is the next step? very confused on where to go from here, the question also states that there is a load factor of 2.. thanks in advance!

Sam

Explanation / Answer

lets assume length of the beam is = L

so, maximum bending moment in the beam will be PxL near to the fixed support (if P is the applied load at the end of the beam)

now,load factor is 2, so our factored load is 2P and factorred moment near to support is 2PL.

now calculate the second moment of area,I=(50x1003/12)-(40x903/12)=1736666.667mm4

Ymax = h/2 = 100/2 = 50mm

now from F=MY/I, here F is stress in the beam at any distance Y from the neutral axis

so for Fmax,

Fmax = (MxYmax) /(I)

now put the value of Fmax= 350MN/m2 = 350x10-6 MN/mm2, M=2PL ,(here value of L should be in mm), Ymax= 50mm and I= 1736666.667mm4

now put all the value in the equation and solve properly you will get your answer in MN, and if not please post the complete question.

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