The document outlines the objectives and key topics of 'mechanics of materials', focusing on the load-carrying capacity of materials through various concepts such as strength, stiffness, and stability. It covers essential concepts and calculations related to axially loaded members, bending and shear, torsion, column buckling, and stress transformation. Important formulas and practical applications in design and structural analysis are also included.

1. Revision for Mechanics of Materials
Dr. Xing Ma
30/04/2024 1

2. What is “Mechanics of Materials”?
Objective: to study load-carrying capacity of a member from the
following standpoints:
• Strength
The ability to resist fracture or permanent deformation.
We need know the maximum stress in the member.
• Stiffness
The ability to resist deflection/deformation.
We need know the maximum strain/deflection in the member.
• Stability
The ability to remain equilibrium configuration.
We need know the critical stress/load of the member.

3. Contents in “Mechanics of Materials”
• Axially loaded members
• Bending and shear (beam theory)
• Torsion
• Column buckling
• Combined loadings
• Indeterminate structures
• Stress transformation

4. Requirement for “Axially loaded
members”
• To understand the concept of normal force and normal
stress
• To be able to calculate the normal stress and normal
deformation
• Important formulas
A
P


AE
PL



5. Requirement for “Bending and shear”
• To understand the concept of bending, shear
• To understand the normal stress due to bending and shear
stress due to shear force
• To be able to draw Shear Force Diagram (SFD), and Bending
Moment Diagram (BMD)
• To be able to draw normal stress distribution (maximum
tensile normal stress and maximum compression normal
stress) due to moment and shear stress (maximum shear
stresses) distribution due to shear force
• To be able to calculate maximum deflection due to lateral
loadings
• To be able to calculate centroid and I values for composite
sections

6. Important formulas for “Bending and shear”
I
My
x 

Flanges
Web
 
VQ
Ib
Deflection for beams
Point Load at mid-span Δ=PL3/(48EI)
Uniform Load Δ=5qL4/(384EI)

7. Centroid and Moment of Inertia
y
x
C
b
dy
h/2
h/2
y
I
bh
I
hb
x y
 
3 3
12 12
,




 n
i
i
n
i
i
i
A
A
x
x
1
1




 n
i
i
n
i
i
i
A
A
y
y
1
1
I I Ad
I I Ad
x xc y
y yc x
 
 
'
'
2
2
C x
y
One axis of symmetry

8. Requirement for “Torsion”
• To understand the distribution of shear stress due to
torque
• To be able to calculate the maximum shear stress using
given formulas
J
Tr


m
avg
tA
T
2



9. Requirement for “Column buckling”
• To understand the concept of column buckling
• To be able to calculate critical load based on given formulas
• To understand the concept of “effective length” due to end
conditions
2
2
e
cr
L
EI
P


Le = KL

10. Requirement for “Combined
loadings”
• To be able to calculate internal actions (normal force,
shear force, bending moment and torque) on a cross
section due to complex loads
• To be able to calculate the maximum compressive and
maximum tensile stress due to combination of normal
force and bending moment
• To be able to calculate maximum shear stress due to
combination of shear force and torque
• Review practical project 4 “design of a signpost”

11. Requirement for “Indeterminate
structures”
• To be able to solve indeterminate problems using combination of
equilibrium equations and compatibility conditions
• To be able to solve the following two types of questions
Q1. One bar with two ends fixed
Q2. Several bars support one rigid beam/plate
A FA
B
C
LAC
LCB
FB
P

12. Requirement for “Stress
transformation”
• To be able to calculate principle stresses using given
formulas
2
2
2
,
1
2
2
xy
y
x
y
x





 







 


