Answered: Compute the stress distribution of the…

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

Compute the stress distribution of the beam shown in the figure at mid-section. Cross-sectional dimensions of the beam is 14in X 40in. If the tensile capacity is 1ksi, comment on stability of the beam.

Expert Solution

Step 1 : Diagram

Step 2 : Reactions

$\begin{array}{rcl} \sum_{} M_{A} & = & 0 \\ 0 & = & - B_{y} \times 60 + 1 \times 60 \times 30 \\ B_{y} & = & 30 k \\ \sum_{} F_{Y} & = & 0 \\ 0 & = & A_{y} - 1 \times 60 + 30 \\ A_{y} & = & 30 k \\ \underset{}{\sum F_{X} = 0} \\ 0 & = & - A_{x} + 200 - 200 \\ A_{x} & = & 0 k \end{array}$

Step 3: Max moment

$\begin{array}{rcl} M o m e n t w i l l b e c r e a t e d b y t r a n s v e r s e l o a d o r v e r t i c a l l o a d . \\ M a x m o m e n t f o r b e a m u n d e r u d l, \\ M_{m a x} & = & \frac{w L^{2}}{8} = \frac{1 \times 60^{2}}{8} \\ = & 450 k . f t \\ M_{m a x} & = & M o m e n t a t m i d - s e c t i o n . \\ F l e x u r a l f o r m u l a : \\ \frac{M}{I} & = & \frac{σ}{y} \\ w h e r e, \\ M & = & B e n d i n g m o m e n t a t p o i n t u n d e r c o n s i d e r a t i o n \\ I & = & M o m e n t o f i n e r t i a o f s e c t i o n \\ σ & = & B e n d i n g s t e s s \\ y & = & D i s \tan c e f r o m N e u t r a l a x i s t o p o i n t w h e r e s t r e s s i s t o b e c a l c u l a t e d . \end{array}$

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