(8%) Problem 8: Consider a square- faced beam supporting a section of a building

Question

(8%) Problem 8: Consider a square- faced beam supporting a section of a building a) b) c) in ©theexpertta.com 33% Part (a) Before installation, the length of the beam is found to be 10 = 15.01 m (figure a). After installation and construction, the 14.93 m (figure b). Determine Young's Modulus Yin N/mz for the beam if it supports a mass m = 37000 length is remeasured and found to be kg and has a side length d - 14m 33% Part (b) If we were to double the dimensions (length and width) of the beam, which of the following are correct 33% Part (c) Suppose that after the beam is installed it needs to be repaired. The weight it supports is removed and replaced with a new mass m2 (figure c). After the new mass is supported, the side length is remeasured and found to be larger with a difference of Ad. Assuming that this side length deformation is uniform and small, write an expression for determining Poisson's ratio v for this beam if its Young's modulus Y i:s known Grade Summary Deductions Potential 100%

Explanation / Answer

(a) We know that young modulus is defined by
E = stress /strain
Stress = force /area = (37000*9.81) /(d)2 = 185188.78 N/m2
Force = mg and area = d2
Now strain = Change in length /original length = (15.01 - 14.93)/15.01 = 5.329*10-3
Now young modulus
E = 185188.78 /5.329*10-3 = 34746044.85 N/m2
(c) We know that the
youung modulus
E = 2G(1+v)
where G is shear modulus and v is poisson ratio
v = (E/2G)- 1

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