Concept explainers
9.29 and 9.30 Determine the reaction at the roller support and the deflection at point C.
Fig. P9.30
Find the reaction at the roller support and the deflection at point C of the beam.
Answer to Problem 30P
The reaction at the roller support B is
The deflection at point C of the beam 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 A;
Substitute 0 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,
Show the free-body diagram of the beam AB as in Figure 3.
Resolve the vertical component of forces as follows;
Take moment about the point A as follows;
Substitute
Therefore, the reaction at the roller support B is
Substitute
Substitute
At point C;
Substitute
Therefore, the deflection at point C of the beam is
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Chapter 9 Solutions
EBK MECHANICS OF MATERIALS
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