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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Determine the slope of end C of the overhang beam. EI is constant.

Expert Solution

Step 1:-

Step 2:-Types of loading in the figures

There are two type of load acting on the body
First is uniform distributed load,it's magnitude will be $P_{1} = W L$ , $a t c e n t r e o f \frac{L}{2}$
Second load is varying distributed load. it's magnitude will be $P_{2} = \frac{1}{2} \times W L$ , $a t a p o i n t \frac{7}{6} L$

Step 3:-Finding reaction for this beam

Applying the equilibrium condition,

$\sum_{1} F_{y} = 0$

$R_{A} + R_{B} = \frac{3}{2} \times W L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)$

$\sum_{1} M_{y} = 0$

$\frac{W L^{2}}{2} + \frac{7}{12} \times W L^{2} = \frac{3}{2} \times R_{B} \times L; R_{B} = \frac{13}{18} \times W L$

Putting value of R_B in the first equation,

$R_{A} = \frac{3}{2} \times W L - R_{B}; R_{B} = \frac{14}{18} \times W L$

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