# Solid Mechanic

To show how to use the method of sections for determining the internal loadings in a member. To introduce the concepts of normal and shear stress. To analyse and design members subject to axial load and direct shear. To define normal and shear strain, and show how they can be determined for various types of problems. Copyright © 2011 Pearson Education South Asia Pte Ltd

In-Class Activities

• • • • • • • • Reading Quiz Applications Normal Stress Shear Stress Normal Strain Shear Strain Cartesian Strain Components Concept Quiz

Copyright © 2011 Pearson Education South Asia Pte Ltd

READING QUIZ

1. What is the normal stress in the bar if P=10 kN and 500 mm²? a) b) c) d) e) 0.02 kPa 20 Pa 20 kPa 200 N/mm² 20 MPa

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READING QUIZ (cont)

2. What is the average shear stress in the internal vertical surface AB (or CD), if F=20 kN, and AAB=ACD=1000 mm²? a) b) c) d) e) 20 N/mm² 10 N/mm² 10 kPa 200 kN/m² 20 MPa

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READING QUIZ (cont)

3. The center portion of the rubber balloon has a diameter of d = 100 mm. If the air pressure within it causes the balloon’s diameter to become d = 125 mm, determine the average normal strain in the rubber. a) b) c) d) 0.2 0.25 π 0.25 1.25

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READING QUIZ (cont)

4. What is the unit of strain?

a) b) c) d) mm mm/m Micron no unit

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APPLICATIONS

Where does the average normal stress occur?

Copyright © 2011 Pearson Education South Asia Pte Ltd

Copyright © 2011 Pearson Education South Asia Pte Ltd

APPLICATIONS (cont)

Will the total shear force over the anchor length be equal to the total tensile force σtensile A in the bar?

Copyright © 2011 Pearson Education South Asia Pte Ltd

APPLICATIONS

Copyright © 2011 Pearson Education South Asia Pte Ltd

AVERAGE NORMAL STRESS

Will the total shear force over the anchor length be equal to the total tensile force σtensile A in the bar?

P A

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NORMAL SHEAR STRESS

Fz z lim A0 A

Fx zx lim A0 A Fy zy lim A0 A

Copyright © 2011 Pearson Education South Asia Pte Ltd

EXAMPLE 1

The bar in Fig. 7-14a has a constant width of 35 mm and a thickness of 10 mm. Determine the maximum average normal stress in the bar when it is subjected to the loading shown.

Copyright © 2011 Pearson Education South Asia Pte Ltd

EXAMPLE 1 (cont)

Solution

• By inspection, different sections have different internal forces.

• Graphically, the normal force diagram is as shown.

Copyright © 2011 Pearson Education South Asia Pte Ltd

EXAMPLE 1 (cont)

Solution

• By inspection, the largest loading is in region BC,

PBC 30 kN

• Since the cross-sectional area of the bar is constant, the largest average normal stress is

BC

PBC 30103 85.7 MPa (Ans) A 0.0350.01

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DESIGN OF SIMPLE CONNECTION • For normal force requirement A P

allow

•

For shear force requirement

A

V

allow

Copyright © 2011 Pearson Education South Asia Pte Ltd

EXAMPLE 2

The rigid bar AB shown in Fig. 1–29a is supported by a steel rod AC having a diameter of 20 mm and an aluminum block having a cross sectional area of 1800 mm2. The 18-mmdiameter pins at A and C are subjected to single shear. If the failure stress for the steel and aluminum is st fail 680 MPaand al fail 70 MPa, respectively, and the failure shear stress for each pin is fail 900 MPa, determine the largest load P that can be applied to the bar. Apply a factor of safety of FS=2.

Copyright © 2011 Pearson Education South Asia Pte Ltd

EXAMPLE 2 (cont)

Solution

• The allowable stresses are

680 340 M Pa F .S . 2 al fail 70 al allow 35...

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