A W 200 x 41.7 wide-flange beam (see Table F-l(b), Appendix F) is simply supported with a span length of 2.5 m (see figure). The beam supports a concentrated load of 100 kN at 0.9 m from support B. At a cross section located 0,7 m from the left-hand support, determine the principal stresses tr, and
(a).
To find: Values of maximum stress and principal shear stress at top of beam.
Answer to Problem 8.4.16P
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
Values of principal normal stress :
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 Principal and normal stress are given by following equation:
Maximum shear stress:
Conclusion:
Hence, we get:
Values of principal stress :
Maximum shear stress
(b).
To find: The values of principal stress and principal stress at top of web.
Answer to Problem 8.4.16P
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
Values of principal normal stress:
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
Values of principal normal stress are given by following equation:
Maximum shear stress,
Conclusion:
Hence, we get:
Values of principal stress :
Maximum shear stress
(c).
To find: Values of principal stress and maximum stress at neutral axis.
Answer to Problem 8.4.16P
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 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
Values of principal stress are given by following equation:
Maximum shear stress:
Conclusion:
Hence, we get:
Values of principal stress:
Maximum shear stress
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Chapter 8 Solutions
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning