Concept explainers
Consider the uniformly loaded simply supported steel beam with an overhang as shown. The second-area moment of the beam is I = 0.05 in4. Use superposition (with Table A–9 and the results of Prob. 4–20) to determine the reactions and the deflection equations of the beam. Plot the deflections.
Problem 4–21
The net reaction at
The net reaction at
The expression for the deflection in the beam of portion
The expression for the deflection in the beam of portion
The plot of deflection verses length of the beam.
Answer to Problem 21P
The net reaction at
The net reaction at
The expression for the deflection in the beam of portion
The expression for the deflection in the beam of portion
The plot of deflection verses length of the beam is
Explanation of Solution
Write the expression for the reaction at
Here, the uniform load on the beam is
Write the expression for the reaction at
Here, the reaction at the
Write the expression for the deflection of the beam between
Here, the moment of inertia of the beam is
Write the expression for the slope of the deflection in the beam.
Substitute
Substitute
Write the expression for the deflection of the beam for
Substitute
Write the expression for the reaction at one end of the overhang section.
Here, the distance between
Write the expression for the reaction at other end of the overhang section.
Write the expression for the deflection in the beam section
Write the expression for the deflection in the beam section
Write the expression for the net reaction at
Write the expression for the net reaction at
Add equation (III) and (XI).
Add equation (VII) and (XII).
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the net reaction at
Substitute
Thus, the net reaction at
Substitute
Thus, the expression for the deflection in the beam of portion
Substitute
Thus, the expression for the deflection in the beam of portion
Substitute different values of
Substitute
Substitute
Similarly,
Use excel spread sheet to calculate the
The Table-(1) shows the different values of the deflection at different point of the beam.
Table-(1)
S. No. | length | deflection |
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 | ||
13 | ||
14 | ||
15 | ||
16 | ||
17 | ||
18 | ||
19 | ||
20 | ||
21 | ||
22 | ||
23 | ||
24 | ||
25 | ||
26 | ||
27 | ||
28 | ||
29 |
Draw the plot of length of the beam verses deflection of the beam.
Figure-(1)
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Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)