Question 9.10: Determine the slope and deflection at end B of the prismatic...
Determine the slope and deflection at end B of the prismatic beam of Example 9.09, drawing the bending-moment diagram by parts.
We replace the given loading by the two equivalent loadings shown in Fig. 9.53, and draw the corresponding bending-moment and (M/EI) diagrams from right to left, starting at the free end B.
Applying the first moment-area theorem, and recalling that u_{A}=0, we write
u _{B}= u _{B / A}=A_{1}+A_{2}=\left(9 \times 10^{-3} m ^{-1}\right)(3 m )-\frac{1}{2}\left(15 \times 10^{-3} m ^{-1}\right)(3 m )
=27 \times 10^{-3}-22.5 \times 10^{-3}=4.5 \times 10^{-3} rad
Applying the second moment-area theorem, we compute the first moment of each area about a vertical axis through B and write
y_{B}=t_{B / A}=A_{1}(1.5 m )+A_{2}(2 m )=\left(27 \times 10^{-3}\right)(1.5 m )-\left(22.5 \times 10^{-3}\right)(2 m )
=40.5 mm -45 mm =-4.5 mm
It is convenient, in practice, to group into a single drawing the two portions of the (M/EI) diagram (Fig. 9.54).
Related Answered Questions
Question: 9.S-P.5
Verified Answer:
Bending Moment. The equation defining the bending ...
Question: 9.S-P.7
Verified Answer:
Principle of Superposition. The given loading ...
Question: 9.13
Verified Answer:
Determination of Point K Where Slope Is Zero. We r...
Question: 9.S-P.12
Verified Answer:
(M/EI) Diagram. We first draw the bending-mome...
Question: 9.8
Verified Answer:
We consider the reaction at B as redundant and rel...
Question: 9.S-P.8
Verified Answer:
Principle of Superposition. The reaction [late...
Question: 9.S-P.9
Verified Answer:
Principle of Superposition. Assuming the axial...
Question: 9.S-P.3
Verified Answer:
Bending Moment. Using the free body shown, we ...
Question: 9.14
Verified Answer:
We consider the couple exerted at the fixed end A ...
Question: 9.9
Verified Answer:
We first draw the free-body diagram of the beam (F...