Answered: Wo -kwo L-

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

See similar textbooks

Related questions

Concept explainers

Question

For the beam and loading shown, determine the equations of the shear and bending-moment curves and the maximum absolute value of the bending moment in the beam, knowing that (a) k= 1, (b) k= 0.5.

Expert Solution

Step 1

Beam with loading is shown in figure,

Any distance x from left-hand side,

$\begin{array}{rcl} w_{x} & = & w \frac{x}{L} \\ F_{x} & = & - \frac{1}{2} x w \frac{x}{L} \\ = & - \frac{1}{2} \frac{w x^{2}}{L} (f o r t o p l o a d) \end{array}$

For bottom load F_x = total load due to kw_o load - load due to kw_o from the right side of x

$= \frac{k w_{0} L}{2} - \frac{1}{2} (L - x) \frac{k w_{0} x}{L} (f o r b o t t o m l o a d)$

Total load at x,

$= \begin{array}{rcl} - \frac{1}{2} \end{array} \begin{array}{rcl} \frac{w x^{2}}{L} \end{array} + (\frac{k w_{0} L}{2} - \frac{1}{2} (L - x) \frac{k w_{0} x}{L}) (1)$

The total moment at x,

$= (\begin{array}{rcl} - \end{array} \begin{array}{rcl} \frac{1}{2} \end{array} \begin{array}{rcl} \frac{w x^{2}}{L} \end{array}) \frac{x}{3} + (\frac{k w_{0} L}{2} - \frac{1}{2} (L - x) \frac{k w_{0} x}{L}) (\frac{2 x}{3}) (2)$

Step 2

For k = 1,

The problem turn in to unform loading on cantilever beam.

Load variation given by,

F_x = -wx; Which gives share force diagram liner slope ,

Max shear force at x = L is F = -wL.

Mx = -w x (x/2) ; Which gives Bending Moment diagram Parabolic variation,

Maximum bending moment at x = L is $M = \frac{w L^{2}}{2}$

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions