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
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/Chap1/16
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
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