Concept explainers
A sign (mass 1700 kg) hangs from the bottom end of a vertical steel girder with a cross-sectional area of 0.012 m2. (a) What is the stress within the girder? (b) What is the strain on the girder? (c) If the girder is 9.50 m long,how much is it lengthened? (Ignore the mass of the girder itself.)
Part(a)
Stress within the girder.
Answer to Problem 42P
Solution:Stress within the girder is found to be
Explanation of Solution
Given: Cross-sectional area,
Mass of sign,
Length of girder,
Young’s Modulus of the steel,
Formula used: Stress can be obtained by:
Where,
Calculation: Stress in girder when it is hanged is given by
Conclusion:Stress within the girder is found to be
Strain in the girder.
Answer to Problem 42P
Solution: Strain value is
Explanation of Solution
Given Cross-sectional area,
Mass of sign,
Length of girder,
Young’s Modulus of the steel,
Stress within the girder is found to be
Formula Used:
Strain is given by
Where,
Calculation:
From Hooke’s law
Conclusion: Strain value is
Part (c)
Change in length of Girder.
Answer to Problem 42P
Solution: The girder is lengthened by
Explanation of Solution
Given:Cross-sectional area,
Mass of sign,
Length of girder,
Young’s Modulus of the steel,
Stress within the girder found to be
Strain value is
Formula used:
Shortened length is given by
Where,
Calculation: Change in length is given by
This is the final length after loading.
The column is shortened by
Conclusion:The girder is lengthened by
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