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9.29 and 9.30 Determine the reaction at the roller support and the deflection at point C.
Fig. P9.29
![Check Mark](/static/check-mark.png)
Find the reaction at the roller support and the deflection at point C of the beam.
Answer to Problem 29P
The reaction at the roller support A is
The deflection at the point C is
Explanation of Solution
Consider a section at a distance x from left end A of the section AC.
Show the free-body diagram of the section AC as in Figure 1.
Determine the moment at the section by taking moment about the section.
Write the second order differential equation as follows;
Here, the moment at the corresponding section is
Substitute
Integrate the equation with respect to x;
Integrate the Equation (2) with respect to x.
Show the free-body diagram of the section BC as in Figure 2.
Determine the moment at the section by taking moment about the section.
Substitute
Integrate the equation with respect to x;
Integrate the Equation (4) with respect to x.
Boundary condition 1:
At the point A;
Substitute 0 for x and 0 for y in Equation (3).
Boundary condition 2:
At the point B;
Substitute L for x and 0 for
Boundary condition 3:
At the point C;
Equate Equation (2) and (4).
Substitute
Boundary condition 4:
At the point C;
Equate Equation (3) and (5).
Substitute
Boundary condition 5:
At the point B;
Substitute L for x, 0 for y,
Therefore, the reaction at the roller support A is
At the point C;
Substitute
Therefore, the deflection at the point C is
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Chapter 9 Solutions
Mechanics of Materials, 7th Edition
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