A W 12 X 14 wide-flange beam (see Table F-l(a), Appendix F) is simply supported with a span length of 120 in. (see figure). The beam supports two anti-symmetrically placed concentrated loads of 7,5 kips each.
At a cross section located 20 in. from the right-hand support, determine the principal stresses (7]and (7\ and the maximum shear stress Tmaw at each of the following locations: (a) the top of the beam, (b) the top of the web, and (c) the neutral axis,
(a).
To find: Values of principal stresses and maximum shear stress at top of beam.
Answer to Problem 8.4.19P
Values of principal stress :
Maximum shear stress
Explanation of Solution
Given Information:
Beam length
Point load
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Principal normal stresses
Maximum shear stress
From equilibrium:
So, bending moment at point
Shear force at point
Moment of inertia:
First moment of area at the top of beam shall be zero,
So, bending stress at top:
And shear stress at that point:
For this situation no stress in
Values of normal stress is given by following equation:
Maximum shear stress:
Conclusion:
Hence, we get:
Values of principal stress:
Maximum shear stress
(b).
To find: Values of principal stresses and maximum shear stress at top of web.
Answer to Problem 8.4.19P
Values of principal stress:
Maximum shear stress
Explanation of Solution
Given Information:
Beam length
Point load
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Principal normal stresses
Maximum shear stress
From equilibrium,
So, bending moment at point
Shear force at point
Moment of inertia:
First moment of area of flange:
So, bending stress at top of web:
And shear stress at that point:
For this situation no stress in
Principal normal stresses are given by following equation,
Maximum shear stress,
Conclusion:
Hence we get,
Principal stresses
Maximum shear stress
(c).
Find principal stresses and maximum shear stress at neutral axis.
Answer to Problem 8.4.19P
Principal stresses
Maximum shear stress
Explanation of Solution
Given Information:
Beam length
Point load
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Principal normal stresses
Maximum shear stress
From equilibrium,
So bending moment at point
Shear force at point
Moment of inertia,
First moment of area for the section above the neutral axis,
So bending stress at neutral axis,
And shear stress at that point,
For this situation no stress in
Principal normal stresses are given by following equation,
Maximum shear stress,
Conclusion:
Hence we get,
Principal stresses
Maximum shear stress
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Chapter 8 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