Concept explainers
9.59 through 9.62 For the beam and loading indicated, determine the magnitude and location of the largest downward deflection.
9.60 Beam and loading of Prob. 9.46.
9.46 For the beam and loading shown, determine (a) the slope at end A, (b) the deflection at point B. Use E = 29 × 106 psi.
Fig. P9.46
Find the magnitude and location of the largest downward deflection of the beam.
Answer to Problem 60P
The location of the largest downward deflection is
The largest downward deflection of the beam is
Explanation of Solution
Given information:
The modulus of elasticity of the material is
Calculation:
Show the free-body diagram of the beam AD as in Figure 1.
Write the singularity equation for load intensity as follows;
Integrate the equation to find the shear force.
By definition, the change in bending moment with respect to change in distance is shear force.
Integrate the equation to find the bending moment.
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.
Boundary condition 1:
At the point D;
Substitute 48 in. for x and 0 for M in Equation (1).
Boundary condition 2:
At the point A;
Substitute 86.667 lb for
Boundary condition 3:
At the point D;
Substitute 86.667 lb for
Determine the moment of inertia (I) of the circular cross section using the equation.
Here, the diameter of the circular cross section is d.
Substitute 1.25 in. for d.
At point A;
Substitute
At point B;
Substitute
At point C;
Substitute
At point D;
Substitute
The slope changes from negative to positive in the section BC.
The maximum deflection occurs where the slope changes sign. i.e.,
Substitute 0 for
Solve the Equation;
Therefore, the location of the largest downward deflection is
At largest deflection point;
Substitute
Therefore, the largest downward deflection of the beam is
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Chapter 9 Solutions
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