# Solid Mechanic

Topics: Force, Continuum mechanics, Shear strain Pages: 11 (1584 words) Published: May 18, 2013
Chapter Objectives
 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

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

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

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

4. What is the unit of strain?
a) b) c) d) mm mm/m Micron no unit

APPLICATIONS
Where does the average normal stress occur?

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

APPLICATIONS

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

NORMAL SHEAR STRESS
Fz  z  lim A0 A
Fx  zx  lim A0 A Fy  zy  lim A0 A

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.

EXAMPLE 1 (cont)
Solution
• By inspection, different sections have different internal forces.

• Graphically, the normal force diagram is as shown.

EXAMPLE 1 (cont)
Solution

PBC  30 kN
• Since the cross-sectional area of the bar is constant, the largest average normal stress is

 BC

PBC 30103     85.7 MPa (Ans) A 0.0350.01

DESIGN OF SIMPLE CONNECTION • For normal force requirement A P

 allow

For shear force requirement

A

V

 allow

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.

EXAMPLE 2 (cont)
Solution
• The allowable stresses are
680  340 M Pa F .S . 2  al  fail 70  al allow    35...