Determine the bending stress at top and bottom of the cross-section withthe moment at 20" to right of point A, and at the mid-span3 in. 3 in. 3 in.6 in.2 in.15 kips15 kipsABD.60 in.→40 in.40 in.

In given beam support reactions R=15 kipsmoment at 20" from A M1=R×20 =15×20=300 kips-inmoment at…

Answered: Determine the bending stress at top and…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Determine the bending stress at top and bottom of the cross-section with
the moment at 20" to right of point A, and at the mid-span
3 in. 3 in. 3 in.
6 in.
2 in.
15 kips
15 kips
A
B
D
.60 in.→
40 in.
40 in.

Expert Solution

Step 1 Solution

$I n g i v e n b e a m s u p p o r t r e a c t i o n s R = 15 k i p s m o m e n t a t 20 " f r o m A M_{1} = R \times 20 = 15 \times 20 = 300 k i p s - i n m o m e n t a t m i d s p a n M_{2} = 15 \times 70 - 15 \times 30 = 600 k i p s - i n D e p t h o f n e u t r a l a x i s f r o m t o p \bar{y} = \frac{A_{1} y_{1} + A_{2} y_{2}}{A_{1} + A_{2}} = \frac{6 \times 3 \times 3 + 9 \times 2 \times 7}{18 + 18} = 5 i n f r o m t o p \Rightarrow M o m e n t o f i n e r t i a a b o u t N . A I_{N A} = I_{x x 1} + I_{x x 2} = \frac{3 \times 6^{3}}{12} + 6 \times 3 \times 2^{2} + \frac{9 \times 2^{3}}{12} + 9 \times 2 \times 2^{2} = 204 i n^{4}$

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