MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
Mechanics
Simple Stress
- may be defined as the science which
- defined as the force per unit area
considers the effects of forces on rigid
bodies
Formula:
Mechanics of deformable bodies
- deals with the relations between
externally applied loads and their
internal effects on bodies
Types of loading resulting in different types
of stress
US
SI Units
Customary
1. Axial Force (P)
Units
- measures the pulling or
pushing action perpendicular to
Force
𝑵
𝒍𝒃
the section
- pull represents a tensile force
Area
𝒎𝟐
𝒊𝒏𝟐
that tends to elongate the
Stress
𝑵/𝒎𝟐
𝒍𝒃/𝒊𝒏𝟐
member
- push is a compressive force
that tends to shorten the
member
Equivalence
2. Shear Force (V)
- components of the total
𝟏 𝑷𝒂 = 𝑵/𝒎𝟐
resistance to sliding the portion
𝟏 𝒑𝒔𝒊 = 𝒍𝒃/𝒊𝒏𝟐
𝟏 𝒌𝒊𝒑 = 𝟏𝟎𝟎𝟎 𝒍𝒃
to one side of the section past
𝟏
𝒌𝒔𝒊 = 𝟏𝟎𝟎𝟎 𝒑𝒔𝒊
the other
3. Bending Moments (M)
- These components measure Three types of simple stresses:
the resistance to bending about
an axis
1. Normal Stress
4. Torque (T)
- The
applied
force
is
- This component measures the
perpendicular to the resisting
resistance to twisting the
area
member
2. Shear Stress
- The applied force is parallel to
Stress
the resisting area
- is defined as the strength of a
3. Bearing Stress
material per unit area
- It is the contact pressure
- it is also called the unit strength
between separate bodies.
Sample Problem 1:
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
A hollow steel tube with an inside diameter of 100 mm must carry a tensile load of
400 kN. Determine the outside diameter of the tube if the stress is limited to 120 𝑀𝑀/𝑀2
Sample Problem 2:
A homogeneous 800 kg bar AB is supported at either end by a cable as shown in Fig. P-105. Calculate the
smallest area of each cable if the stress is not to exceed 90 MPa in bronze and 120 MPa in steel.
Sample Problem 3:
The homogeneous bar shown in Fig. P-106 is supported by a smooth pin at C and
a cable that runs from A to B around the smooth peg at D. Find the stress in the cable if
its diameter is 0.6 inch and the bar weighs 6000 lb.
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
Sample Problem 4:
The homogeneous bar shown in Fig. P-106 is supported by a smooth pin at C and
a cable that runs from A to B around the smooth peg at D. Find the stress in the cable if
its diameter is 0.6 inch and the bar weighs 6000 lb.
SHEAR STRESS:
Sample Problem 1:
Find the smallest diameter bolt that can be used in the clevis shown in the figure
if P = 400 kN. The shearing strength of the bolt is 300 MPa.
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
Sample Problem 2:
A 200-mm-diameter pulley is prevented from rotating relative to 60-mm-diameter shaft by a
70-mm-long key, as shown in Fig. P-118. If a torque T = 2.2 kN·m is applied to the shaft,
determine the width b if the allowable shearing stress in the key is 60 MPa.
Sample Problem 3:
The members of the structure in Fig. P-120 weighs 200 lb/ft. Determine the
smallest diameter pin that can be used at A if the shearing stress is limited to 5000 psi.
Assume single shear.
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
Sample Problem 4:
What force is required to punch a 20-mm-diameter hole in a plate that is 25 mm
thick? The shear strength is 350 MN/m2.
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
BEARING STRESS:
Sample Problem 1:
In the clevis shown in Fig. 1-11b, find the minimum bolt diameter and the
minimum thickness of each yoke that will support a load P = 14 kips without exceeding a
shearing stress of 12 ksi and a bearing stress of 20 ksi.
Sample Problem 2:
In Fig. 1-12, assume that a 20-mm-diameter rivet joins the plates that are each
110 mm wide. The allowable stresses are 120 MPa for bearing in the plate material and
60 MPa for shearing of rivet. Determine (a) the minimum thickness of each plate; and
(b) the largest average tensile stress in the plates.
MECHANICS OF DEFORMABLE BODIES SAMPLE PROBLEMS
Sample Problem 3:
The lap joint shown in Fig. P-126 is fastened by four ¾-in.-diameter rivets. Calculate the
maximum safe load P that can be applied if the shearing stress in the rivets is limited to 14 ksi
and the bearing stress in the plates is limited to 18 ksi. Assume the applied load is uniformly
distributed among the four rivets.