A sign (mass 2200 kg ) hangs from the end of a vertical steel girder with a cros

Question

A sign (mass 2200 kg ) hangs from the end of a vertical steel girder with a cross-sectional area of 0.010 m2 . Ignore the mass of the girder itself. The elastic modulus for steel is 2.0×1011N/m2 .

Part A

What is the stress within the girder?

Express your answer to two significant figures and include the appropriate units.

Part B

What is the strain on the girder?

Express your answer to two significant figures.

Part C

If the girder is 7.20 m long, how much is it lengthened?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Assuming Modulus of Elasticity for Steel = 2 * 10^11N / m^2

A=0.010m^2

m=2200kg

length=7.2m


(a) What is the stress within the girder?

stress = Force / cross -sectional area = (2200*9.81) / 0.01 = 2.16*10^6 N / m^2

(b) What is the strain on the girder?
Strain = Stress / Young's modulus = (2158200) / ( 2* 10^11) = 1.08* 10^-5

c) If the girder is 7.2 m long, how much is it lengthened?
elongation = strain x length = 1.08* 10^-5* 7.2= 7.78*10-5 m

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