Strength_Materials_Lecture1.pdf for Vietnamese student

Introduction to Strength of Materials

1. Strength of Materials
Sức Bền Vật Liệu
Lecture 1: Introduction
2023

2. Aerodynamics
Structures
Flight Mechanics Propulsion
Aeronautical
Engineering

3. Introduction
Giới thiệu
The study of Strength of
Materials studies materials,
structures, loads, deformations,
failures and how to prevent
failures through analysis and
design.
Môn học Sức Bền Vật Liệu
nghiên cứu các loại vật liệu, cấu
trúc, lực, biến dạng, hỏng hóc
và cách phòng ngừa hỏng hóc
thông qua phân tích và thiết kế.

4. •R.C. Hibbeler, Mechanics of Materials, 8th Edition, Pearson
Prentice Hall, 2011
•Robert L. Mott, Joseph A. Untener, Applied Strength of Materials,
6th Edition, CRC Press, 2017
•Đỗ Kiến Quốc, Sức bền vật liệu, Nhà xuất bản ĐHQG TP.HCM
2004
•Bùi Trọng Lựu, Nguyễn Văn Vượng, Bài tập sức bền vật liệu,
Nhà xuất bản Giáo dục, 1999
Books

5. •It’s all about safety awareness in structural analysis and
design.
•Machine, product, structure must be safe and stable under
the loads exerted on it during any foreseeable use
•The material may deform excessively under load or could
fracture completely
•The structure could become unstable and buckle
•Examples of these failure modes should help you to understand
the importance of the principles of applied strength of materials
Mục tiêu của môn học
Objectives of this course

6. •You will be able to identify different components of a structure:
loads, deformations, stresses, strains
•You will be able to predict the failures and the instabilities of a
structure
•You will be able to design some structures to work safely
•You will differentiate different engineering standards in different
countries
Learning Outcomes

7. Examples of applications

8. Example of applications

9. •Basic nature of stresses and strains
•Types of stresses created by different loading and support
situations
•Analyze situations where more than one kind of stress is
experienced by a load-carrying member at the same time
•Determining shape and size of a load-carrying member and
specify the material from which it is to be made
•Designing safe load-carrying components of machines and
structures
What will we learn?

10. Examples of Loads and Deformations
Simple Tension/Compression
Tension Compression

11. Examples of Loads and Deformations
Buckling and shear
Buckling Shear

12. Examples of Loads and Deformations
Bending and Twisting
Twisting
Bending

13. Failure modes
Fracture
•How much weight do the
rods carry?
•What material should they
be made of?
•How strong is the material
of the rods?

14. Failure modes
Excessive deformation
•F1 and F2 tend to pull the
gears apart: misalignment
•How to prevent?

15. Failure modes
Buckling
•Slender column subjected
to compression force
•Not a material failure but
instability

16. Basic Unit Systems
SI metric unit system and U.S. Customary unit system
Basic quantities in the SI metric unit system
Basic quantities in the US Customary unit system
Conversion factors?

17. Basic Unit Systems
Prefixes for SI units
Proper method of reporting computed quantities

18. •Mass refers to the amount of
the substance in a body
•Force is a push or pull effort
exerted on a body either by an
external source or by gravity
•Weight is the force of
gravitational pull on a body
Khối lượng, Lực và Trọng lượng
Mass, Force and Weight

19. Density and Specific Weight
Khối lượng riêng và Trọng lượng riêng
Density is the amount of mass
per unit volume of a material
Specific weight is the amount of
weight per unit volume of a
material
Symbol: ρ
Units: slugs/ft
3 or kg/m
3
Symbol: γ
Units: lb/ft
3 or N/m
3

20. Stress (Ứng suất)
Definition
•The study of strength of materials
depends on an understanding of
the principles of stress and
strain produced by applied
loads on a structure or a machine
•Stress is the internal resistance
offered by a unit area of the
material from which a member is
made to an externally applied
load
Stress vs. Pressure
Same same but different

21. Stress (Ứng suất)
Definition
•Uniformly distributed stress:
the same magnitude at any
point in the cross section

•Uneven distributed stress:
different magnitudes at
different points in the cross
section
σ=
dF
dA

22. •Strain is the deformation per unit length of the member, also known as “unit
deformation”
•Deformation can be a result of applied loads or temperature changes
•Strain is dimensionless, but it can be reported as in/in or mm/mm to reflect
deformation per unit length
•Stress - strain relationship follows Hooke’s law in elastic material
•E is the stiffness of material or modulus of elasticity or Young’s modulus
Definition
Strain (Độ Biến dạng)

23. Example
Strain

24. Example of Hooke’s law
Stress - strain relationship
How to get
these charts?
Why?

25. •Normal stress (σ): perpendicular, or normal, to the cross
section of the load-carrying member.
•One of the most fundamental types of stress
•If the stress is uniform across the resisting area, the stress is
called a “direct normal stress”.
Definition
Direct Normal Stress - Ứng suất pháp trực tiếp

26. Compressive (Nén) and Tensile (Kéo) Stress
Direct Normal Stress
Compressive stress: tends to
crush the material and
shorten the member
Tensile stress: tends to pull
the material apart and stretch
the member

27. Direct Normal Stress
Example Problem
Solution:
Objective: Compute the stress in
the support rods
Given: Casting weighs 11.2 kN.
Each rod carries half the load.

Rod diameter = D = 12.0 mm
Analysis: Direct tensile stress is
produced in each rod
Problem:
Two circular rods carrying a
casting weighing 11.2 kN. If each
rod is 12.0 mm in diameter and
the two rods share the load
equally, compute the stress in the
rods

28. Direct Normal Stress
Example Problem
Solution:
Objective: Compute the stress in the upper
part of the stand.
Given: Load = F = 27 500 lb; load is centered
on the stand.

The cross section is square; the dimension of
each side is 1.50 in
Analysis: Internal resisting force that acts
upward to balance the downward applied
load on any cross section.

Uniformly distributed internal force.

Compressive stress.
Problem:
Compute the stress in the square shaft at the
upper part of the stand for a load of 27 500
lb. The line of action of the applied load is
centered on the axis on the shaft, and the
load is applied through a thick plate that
distributes the force to the entire cross
section of the stand.

29. •Infinitesimal element inside the member: cube (3D) or square (2D)
•A net force acting on the top and bottom faces of the cube
•Consider the faces to be unit areas (đơn vị diện tích) : forces ~
stresses
•Equilibrium (cân bằng) element: stresses on the top and the
bottom are the same
Stress Elements - Phần tử ứng suất
Direct Normal Stress

30. •Shear stress (ứng suất cắt/trượt) or tangential (tiếp tuyến) stress
(τ): parallel (tangential) to the cross section of the load-carrying
member
•Causes layers or parts to slide upon each other in opposite
directions
•Example: the force of two connecting rocks rubbing in opposite
directions
•A uniform level of shearing force across the entire area being
sheared: direct shear stress
Definition
Direct Shear Stress - Ứng suất tiếp trực tiếp

31. Direct Shear Stress
Example Problem
Solution:
Objective: Compute the shear stress in
the material.
Given: F = 1250 lb; t = 0.040 in.
Analysis: The sides of slug are placed in
direct shear resisting the applied force.
Problem:
Compute the shear stress in the
material if a force of 1250 lb is
applied through the punch. The
thickness of the material is 0.040 in.
Note:
•A punching operation: the objective is
to actually cut one part of the material
from the other
•The punching action produces a slot in
the flat sheet metal. The part removed
in the operation is sometimes called a
“slug”
•The shearing action occurs along the
sides of the slug, shown in blue

32. Example of Direct Shear Stress
Single Shear
Solution:
Objective: Compute the shear stress in the
pin.
Given: F = 3550 N; D = 10.0 mm
Analysis: The pin is in direct shear with one
cross section of the pin resisting all of the
applied force (single shear).
Problem:
The force on the link in the simple
pin joint is 3550 N. If the pin has
a diameter of 10.0 mm, compute
the shear stress in the pin.
Note:
•A pin or a rivet is often inserted into a
cylindrical hole through mating parts to
connect them.
•When forces are applied perpendicular
to the axis of the pin, there is the
tendency to cut the pin across its cross
section, producing a shear stress
•A single cross section of the pin resists
the applied shearing force

33. Example of Direct Shear Stress
Double Shear
Problem (homework):
The force on the link in the double
pin joint is 3550 N. If the pin has a
diameter of 10.0 mm, compute
the shear stress in the pin.
Note:
•In this design, there are two
cross sections to resist the
applied force
•The pin is in double shear

34. Example of Direct Shear Stress
Keys
•Application of shear in mechanical
drives: a power transmitting element,
such as a gear, chain sprocket, or
belt pulley, is placed on a shaft, a
key is often used to connect the two
and permit the transmission of
torque from one to the other.
•The torque produces a tangential
force at the interface between the
shaft and the inside of the hub of the
mating element.
Problem (homework):
If a torque of 1500 lb·in. is transmitted
from the shaft to the hub, compute the
shear stress in the key. For the
dimensions of the key, use L = 0.75 in.; h
= b = 0.25 in. The diameter of the shaft is
1.25 in.

35. •Infinitesimal element inside the member: cube (3D) or square
(2D)
•The shear stresses acting parallel to the surfaces of the cube
•Equilibrium element: stresses on the top and the bottom are the
same
•To balance the rotation: a pair of equal shear stresses is
developed on the vertical sides of the stress element
Stress Elements - Phần tử ứng suất
Direct Shear Stress

36. •Statical equilibrium
conditions yield:
τ
zy
=τ′
zy
=τ
yz
=τ′
yz
=τ
Complementary Shear Stress
All four shear stresses
must have equal
magnitude and be directed
either toward or away from
each other at opposite
edges of the element

37. •Deformations not only cause line segments to elongate or
contract, but they also cause them to change direction.
•Shear strain is the distortion produced by shear stress on an
element: change in angle between two line segments
•Shear strain is dimensionless and measured in radians
Độ biến dạng cắt/trượt
Shear Strain

38. Shear Strain
γ=
π
2
−θ
: Positive shear strainθ<
π
2
: Negative shear strainθ>
π
2

39. Three methods of structural analysis:
•Analytical analysis (phân tích giải tích): exact solution, but
difficult in complex structures
•Experimental analysis: practical solution, required equipment
•Computational analysis: approximation solution
Question: Which method is preferred?
Phân tích Thực nghiệm và Tính toán số
Experimental and Computational Analysis

40. Experimental Analysis
Photoelastic stress analysis
•Photoelasticity describes changes
in the optical properties of a
material under mechanical
deformation. It is a property of all
dielectric media and is often
used to experimentally determine
the stress distribution in a
material, where it gives a picture
of stress distributions around
discontinuities in materials.
•The material is typically a
transparent plastic that is
illuminated while being loaded.
•In complex structures:
photoelastic coating applied
•Video: https://youtu.be/
vDZ5yISiADM

41. Experimental Analysis
Strain Gage
•Electrical resistance strain
gage: very thin metal foil grid
made from a strain- sensitive
material, such as constantan,
with an insulating backing
•The gage is carefully applied
with a special adhesive to the
surface of the component
where critical stresses are
likely to occur.
•When the component is
loaded, the gage experiences
the same strains as the
surface. The resistance of the
gage changes in proportion to
the applied strain

42. Computational analysis
Finite Element Analysis
•3D/2D modeling by CAD
•Dividing the body into
small elements
•Loads, boundary
conditions, material
properties
•Various software available

43. Next Lesson
Design Properties of Materials