Answered: In the structure shown, the support at…

Fundamentals Of Construction Estimating

4th Edition

ISBN:9781337399395

Author:Pratt, David J.

Publisher:Pratt, David J.

Chapter3: Measuring Quantities Generally

Section: Chapter Questions

Problem 17RQ

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Question

In the structure shown, the support at A rotates 3x10^-3radians CCW, and the support at C has a settlement of 0.8 inches. Make the shear force and bending moment diagram using

1. Three-moment equation

2. Slope Deflection Method

Make sure the diagrams for both methods are the same.

E=29,000 kips per square inch
I=144 in
A
B
12 feet
15 feet

Expert Solution

Step 1

Given

$E = 29000 k i p s / i n^{2} I = 144 i n^{2} Q_{A} = 3 \times 10^{- 3} r a d ∆_{c} = - 0.8 i n A n t i c l o c k w i s e M_{A B} = 0 Q_{A} = 0, ∆_{B} = + 0.8 i n c l o c k w i s e$

Step 2

$M_{A B} = M_{A B} + \frac{2 E I}{L} (2 Q_{A} + Q_{B} - \frac{3 ∆}{L}) M_{A B} = 0 + \frac{2 \times 29000 \times 144}{12} (0 + Q_{B} - \frac{0.8 \times 3}{12}) M_{A B} = 696000 Q_{B} - 139200 \dots \dots \dots (1) M_{B A} = M_{B A} + \frac{2 E I}{L} (2 Q_{B} + Q_{A} - \frac{3 ∆}{L}) M_{B A} = 0 + \frac{2 \times 29000 \times 144}{12} (2 Q_{B} + 0 - \frac{0.8 \times 3}{12}) M_{B A} = 1390000 Q_{B} - 139200 \dots \dots \dots (2) M_{B C} = M_{B C} + \frac{2 E I}{L} (2 Q_{B} + Q_{A} - \frac{3 ∆}{L}) M_{B C} = 0 + \frac{2 \times 29000 \times 144}{15} (2 Q_{B} + Q_{c} - \frac{0.8 \times 3}{15}) M_{B C} = 556800 (2 Q_{B}) - 556800 Q_{c} + 89088 \dots \dots \dots (3) M_{C B} = M_{C B} + \frac{2 E I}{L} (2 Q_{c} + Q_{B} - \frac{3 ∆}{L}) M_{C B} = 0 + \frac{2 \times 29000 \times 144}{15} (2 Q_{C} + Q_{B} - \frac{0.8 \times 3}{15}) M_{C B} = 1113600 Q_{C} + 556800 Q_{B} - 89088 \dots \dots \dots (2)$

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In the structure shown, the support at A rotates 3x10-3 radians CCW, and the support at C has a settlement of 0.8 inches. Make the shear force and bending moment diagram using 1. Three-moment equation 2. Slope Deflection Method Make sure the diagrams for both methods are the same