## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Tip our Team

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

## Holooly Tables

All the data tables that you may search for.

## Holooly Help Desk

Need Help? We got you covered.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

## Q. 7.1

A steel plate of width 120 mm and of thickness 20 mm is bent into a circular arc of radius 10 m. Determine the maximum stress induced and the bending moment which will produce the maximum stress. Take $E = 2 × 10^5 N/mm^2$.

## Verified Solution

Given :
Width of plate,            b = 120 mm
Thickness of plate,     t = 20 mm
∴ Moment of inertia, $I=\frac{b t^3}{12}=\frac{120 \times 20^3}{12}=8 \times 10^4 mm^4$
Radius of curvature,  R = 10 m = 10 × 10³ mm
Young’s modulus,       $E = 2 × 10^5 N/mm^2$
Let                                  $σ_{\max}$ = Maximum stress induced, and
M = Bending moment.

Using equation (7.2),      $\frac{\sigma}{y}=\frac{E}{R}$

∴                                          $\sigma=\frac{E}{R} \times y$    …(i)

Equation (i) gives the stress at a distance y from N.A.
Stress will be maximum, when y is maximum. But y will be maximum at the top layer or bottom layer.

∴                        $y_{\max }=\frac{t}{2}=\frac{20}{2}=10 mm.$

Now equation (i) can be written as

$\sigma_{\max }=\frac{E}{R} \times y_{\max } \\ \space \\ =\frac{2 \times 10^5}{10 \times 10^3} \times 10= \pmb{2 0 0 N / m m ^2 .}$

From equation (7.4), we have
(7.4):          $\frac{M}{I}=\frac{\sigma}{y}=\frac{E}{R}$

$\frac{M}{I}=\frac{E}{R}$

∴                  $M=\frac{E}{R} \times I=\frac{2 \times 10^5}{10 \times 10^3} \times 8 \times 10^4 \\ \space \\ \quad \quad \quad \quad =16 \times 10^5 N mm = \pmb{1 . 6 k N m.}$