Use the worked example above to help you solve this problem. A vertical steel be

Question

Use the worked example above to help you solve this problem. A vertical steel beam in a building supports a load of 5.9 104 N. (a) If the length of the beam is 4.0 m and its cross-sectional area is 7.0 10-3 m2, find the distance the beam is compressed along its length. m (b) What maximum load in newtons could the steel beam support before failing? N EXERCISE HINTS: GETTING STARTED | I'M STUCK! A cable used to lift heavy materials like steel I-beams must be strong enough to resist breaking even under a load of 2.2 106 N. For safety, the cable must support twice that load. (a) What cross-sectional area should the cable have if it's to be made of steel? m2 (b) By how much will a 9.0-m length of this cable stretch when subject to the 2.2 106-N load? m

Explanation / Answer

(a)Since the veertical member is supporting the load 5.9*104 N
therefore
Compressed distance (d)= PL/AE where P is load , L is length , A is area and E is young's modulus
Since Value of E is not mentioned therefore I am using standard value of E , if you have different then please use that.
Using E = 210 GPa
d = (5.9*104*4) /(7*10-3*210*109) = 0.160*10-3 m
(b) Max load supported by the beam is
P = nPi2EI / L2   where I is the moment of inertia
I = Pi*D4/64 =
Since area is given therefore we will calculate D (diameter)from there
Area = (Pi/4)D2
D = 0.0089 m
Pcrtical = 40.123 n N
where n is the index of end condition
if beam is fixed at both ened then we use n =4
for hinged at both end then n = 1

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