A beam ABC with an overhang from B to C is constructed of a C 10 × 30 channel section with flanges facing upward (sec figure). The beam supports its own weight (30 lb/ft) plus a triangular load of maximum intensity g0 acting on the overhang. The allowable stresses in tension and compression arc IS ksi and 12 ksi, respectively.
- Determine the allowable triangular load intensity allow if tne distance L equals 4 ft.
(a)
The allowable triangular load intensity.
Answer to Problem 5.6.11P
The allowable triangular load intensity is
Explanation of Solution
Given information:
The weight of the beam is
The following figure shows the free body diagram.
Figure-(1)
Write the expression for the moment about point
Here, the vertical reaction on point
Write the expression for the equilibrium forces at point
Here, the vertical reaction on point
Write the expression for the maximum moment at point
Here, the maximum moment is
Write the expression for the allowable bending moment based on tension.
Here, maximum tensile stress is
Write the expression for the allowable bending moment based on compression.
Here, maximum compressible stress is
Write the expression for the load intensity of triangular load considering tension.
Write the expression for the load intensity of triangular load considering compression.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The allowable triangular load intensity is
(b)
The allowable triangular load intensity when the beam is rotated
Answer to Problem 5.6.11P
The allowable triangular load intensity when the beam is rotated
Explanation of Solution
Write the expression for the allowable bending moment based on tension.
Write the expression for the allowable bending moment based on compression.
Write the expression for the load intensity of triangular load considering tension.
Write the expression for the load intensity of triangular load considering compression.
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The allowable triangular load intensity when the beam is rotated
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Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning