Concept explainers
The roof beams of a warehouse are supported by pipe columns (see figure) having an outer diameter d2= 100 mm and inner diameter d2, = 90mm. The columns have a length L = 4.0 m, modulus E = 210 GPa, and fixed supports at the base.
Calculate the critical load Pcrof one of the columns using the following assumptions: (a) the upper end is pinned and the beam prevents horizontal displacement; (b) the upper end is fixed against rotation and the beam prevents horizontal displacement; (c) the upper end is pinned, but the beam is free to move horizontally; and (d) the upper end is fixed against rotation, but the beam is free to move horizontally.
i.
The critical load when the upper end is pinned and the beam prevents horizontal displacement.
Answer to Problem 11.4.10P
The critical load when the upper end is pinned and the beam prevents horizontal displacement is 447 kN
Explanation of Solution
Given:
E=210 GPa
L= 4 m
d1= 90 mm
d2= 100 mm
Concept Used:
Calculation:
Conclusion:
The critical load for the pinned-pinned condition is 447 kN
ii.
The critical load when the upper end is fixed for rotation and the beam prevents horizontal displacement.
Answer to Problem 11.4.10P
The critical load when the upper end is fixed for rotation and the beam prevents horizontal displacement is 875 kN
Explanation of Solution
Given:
E=210 GPa
L= 4 m
d1= 90 mm
d2= 100 mm
Concept Used:
Calculation:
Conclusion:
The critical load when the upper end is fixed for rotation and the beam prevents horizontal displacement is 875 kN
iii.
The critical load when the upper end is pinned but beam free to move horizontally.
Answer to Problem 11.4.10P
The critical load when the upper end is pinned but beam free to move horizontally is 54.7 kN
Explanation of Solution
Given:
E=210 GPa
L= 4 m
d1= 90 mm
d2= 100 mm
Concept Used:
Calculation:
Conclusion:
The critical load when the upper end is pinned but beam free to move horizontally is 54.7 kN .
iv.
The critical load when the upper end is fixed under rotation but the beam is free to move horizontally.
Answer to Problem 11.4.10P
The critical load when the upper end is fixed under rotation but the beam is free to move horizontally is 219 kN
Explanation of Solution
Given:
E=210 GPa
L= 4 m
d1= 90 mm
d2= 100 mm
Concept Used:
Calculation:
Conclusion:
The critical load when the upper end is fixed under rotation but the beam is free to move horizontally is 219 kN.
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Chapter 11 Solutions
Mechanics of Materials - Text Only (Looseleaf)
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