Concept explainers
For the beam and loading shown, determine (a) the slope at point B, (b) the deflection at point D. Use E = 200 GPa.
Fig. P9.128
The magnitude
Answer to Problem 146P
The magnitude
Explanation of Solution
Given information:
The section of the beam is
The young’s modulus of steel is
Calculation:
Show the free body diagram of the beam as in Figure 1.
Calculate the vertical reaction at point A by taking moment about point B.
Refer Appendix C “Properties of rolled steel shape (SI units)” for moment of inertia of section
Calculate the value (EI):
Substitute
Calculate the moment due to the reaction at A:
Substitute
Calculate the
Substitute
Show the
Calculate the area
Substitute
Calculate the moment due UDL:
Substitute
Calculate the
Substitute
Show the
Calculate the area
Substitute
Calculate the moment due to the point load at D as below:
Substitute
Calculate the
Substitute
Show the
Calculate the area
Substitute
Calculate the tangential deviation of B with respect to A using the relation:
Substitute
Calculate the slope
Substitute
Let point K is the maximum deflection.
Calculate the moment due to the reaction at A as below:
Substitute
Calculate the
Substitute
Calculate the moment due UDL:
Calculate the
Substitute
Show the
Calculate the area
Substitute
Calculate the area
Substitute
Calculate the slope
Substitute
Differentiate the Equation (1).
Solve the value
Iteration 1:
Substitute 3 for
Substitute 3 for
Iteration 2:
Calculate the value
Substitute 3 for
Similarly calculate the value
f | ||
3 | 28.08 | -72 |
3.39 | -6.78 | -107.8 |
3.327 | -0.188 | -101.6 |
3.3251 | 0.005 | -101.42 |
3.32514 | 0.0001 |
The value of
Calculate the slope at the end A related to the point K
Substitute
Calculate the magnitude
Substitute
Thus, the magnitude
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Chapter 9 Solutions
Mechanics of Materials, 7th Edition
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