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A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L = 1.75 m, and the height of the bar is h = 140 mm. The deflection at the midpoint is measured as 2.5 mm. (a) What is the maximum normal strain £ at the top and bottom of the bar? (b) If allowable strain e a = 0.0006 and the deflection cannot exceed 4.3 mm, what is the maximum permissible length of the bar?

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

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Section
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 5, Problem 5.4.6P
Textbook Problem
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A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L = 1.75 m, and the height of the bar is h = 140 mm. The deflection at the midpoint is measured as 2.5 mm.

(a) What is the maximum normal strain £ at the top and bottom of the bar?

(b) If allowable strain ea= 0.0006 and the deflection cannot exceed 4.3 mm, what is the maximum permissible length of the bar?

  Chapter 5, Problem 5.4.6P, A bar of rectangular cross section is loaded and supported as shown in the figure. The distance

(a)

To determine

The maximum normal strain at the top and bottom of the bar.

Explanation of Solution

Given Information:

  

  L=1.75mh=140mmδ=2.5mm

Formula used:

  ε=h2ρ

  δ=ρ(1cosθ)

  δ=ρ(1cos(L2ρ))

Calculation:

We know that:

  ε=h2ρ=h2ρ ;

And we also know that the formula for the deflection is, δ

(b)

To determine

The maximum permissible length of the bar for the given parameters.

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