MCB 2034 SOLID MECHANICS

January 14, 2014

Chapter 1: Stress

Chap 1 : StressSK/Chap1/2

Learning Outcomes:

At the end of this chapter, students should be able to:

• Determine the internal resultant loadings by applying

methods of sections and equations of equilibrium

• Determine the average normal and average shear

stresses in loaded members

• Produce a safe design by incorporating the concepts of

allowable stresses and factors of safety

WHAT IS ENGINEERING MECHANICS?

Branch of physical sciences – concerned with state of REST or MOTION of bodies – subjected to forces

Study of what happens to a “thing” (the technical name is “body”) when FORCES are applied to it.

The body or the forces could be large or small.

BRANCHES OF MECHANICS

Statics Dynamics

Rigid Bodies

(Things that do not change shape)

Deformable Bodies

(Things that change shape)

Incompressible Compressible

Fluids

Mechanics

Solid Mechanics

Solid Mechanics

Other names:

Mechanics of Deformable Bodies

Strength of Materials

Mechanics of Materials

Definition: A branch of engineering mechanics that studies the internal effects of stress and strain in a solid body the is subjected to an external loading.

Review Statics

Equations of Equilibrium

It must be satisfied in order to prevent a body from translating and rotating

0M

0M

0M

0F

0F

0F

0F

Z

Y

X

Z

Y

X

0M

0F

0F

O

Y

X

Review Statics

Support Reactions

If the support prevents translation in a given direction, then the reaction force must be developed

If rotation is prevented, then a couple moment must be exerted on the member

Internal Resultant Loadings

Practice

Chap 1 : StressSK/Chap1/10

1.1 Introduction

Stress

• intensity of the internal forces distributed over a given section (area)

• basic units:

N/m2 or pascal

psi (pounds per square inch)

• prefixes used for units :

kilo, k (103)

mega, M (106)

giga, G (109)

Chap 1 : StressSK/Chap1/11

A

Fz

Az

0lim

A

F

A

F

y

Azy

x

Azx

0

0

lim

lim

• Normal Stress – Force per unit

area acting normal to A

• Shear Stress – Force per unit

area acting tangent to A

SK/Chap1/12

Chap 1 : Stress

1.2 Average Normal Stress

where

= average normal stress

P = internal resultant normal force

A = cross-sectional area

A

P

SK/Chap1/13

Chap 1 : Stress

Example 1

The bar in Figure E1 has a constant width of 35mm and a thickness of

10mm. Determine the maximum average normal stress in the bar when

it is subjected to the loading shown.

Figure E1

SK/Chap1/14

Chap 1 : Stress

1.3 Average Shear Stress

where

avg = average shear stress

V = internal resultant shear force

A = cross-sectional area

A

Vavg

SK/Chap1/15

Chap 1 : Stress

2 different types of shear:

(a) Single shear

(b) Double shear

SK/Chap1/16

Chap 1 : Stress

Example 2

The bar shown in Figure E2 has a square cross section for which the depthand thickness are 40mm. If an axial force of 800N is applied along thecentroidal axis of the bar’s cross-sectional area, determine the averagenormal stress and average shear stress acting on the material along

(a) section plane a-a (b) section plane b-b

Figure E2

Practice

Determine the internal normal force, shear force, and bending moment at point C.

SK/Chap1/21

Chap 1 : Stress

1.4 Allowable Stress

or

where

allow, allow = allowable stress

fail, fail = failure stress

n = safety factor

n

fail

allow

n

fail

allow

SK/Chap1/22

Chap 1 : Stress

1.5 Design of Simple Connections • Member subjected to normal force

where, A = required area of the section

P = normal force

• Member subjected to shear force

where, A = required area of the section

V = shear force

allow

PA

allow

VA

SK/Chap1/23

Chap 1 : Stress

Example 3

The control arm is subjected to

the loading shown in Figure E3.

Determine to the nearest 5 mm

the required diameter of the steel

pin at C if the allowable shear

stress for the steel is allow = 55

MPa. Note in the figure that the

pin is subjected to double shear.

Figure E3

Free Body Diagram