Lecture-02 Introduction to Shearing, Bearing and Maximum Stresses

8/3/2019 Lecture-02 Introduction to Shearing, Bearing and Maximum Stresses

1/29

STRESS ANALYSISDR. MUHAMMAD ABID

ASSOCIATE PROFESSOR - FME

TOPIC

GIK Institute of Engineering Sciences and Technology

LECTURE

1Introduction

Stress StrainConcepts2


2/29

GIK Institute of Engineering Sciences and Technology. L2 - 2

Shearing Stress

Under applied Forces are applied transverse forces P and

Pto the memberAB, Corresponding internal forces act inthe plane of section Cand are called shearing forces.

A

Pave

The corresponding average shear stress is,

The resultant of the internal shear force distribution is

defined as the shearof the section and is equal to the load P.

A

F

A

P

ave

Single ShearA

F

A

P

2ave

Double Shear
http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/


3/29


Bearing Stress in Connections

Bolts, rivets, and pins create

stresses on the points of contact

or bearing surfaces of the

members they connect.

dt

P

A

Pb

Corresponding average force

intensity is called the bearing

stress,

The resultant of the force

distribution on the surface isequal and opposite to the force

exerted on the pin.


4/29


Determine the stresses in the

members and connections of

the structure shown.

Stress Analysis & Design Example

Normal stresses:

Rod is in tension

Boom is in compression

Shearing stresses:

Pin C is in single shear

Pin A is in double shear

Pin B is in _______ shear

Bearing stress

At A in the boom AB, 53.3

MPa

At C in Bracket 32 MPa


5/29


cossin

cos

sin

cos

cos

cos

00

2

00

A

P

A

P

A

V

A

P

A

P

A

F

The average normal and shear stresses on

the oblique plane are

Stress on an Oblique Plane

sincos PVPF

Resolve P into components normal and

tangential to the oblique section,
http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/


6/29


The maximum normal stress occurs when the

reference plane is perpendicular to the memberaxis,

0

0

m A

P

The maximum shear stress occurs for a plane at

+ 45o with respect to the axis,

00 2

45cos45sinA

P

A

Pm

Maximum Stresses

cossincos0

2

0 A

P

A

P

Normal and shearing stresses on an oblique

plane


7/29GIK Institute of Engineering Sciences and Technology. L2 - 7

Normal Strain and Stress-Strain Diagram

strainnormal

stress

L

A

P

Brittle Materials

Ductile Materials



Hookes Law: Modulus of Elasticity

Below the yield stress

ElasticityofModulus

orModulusYoungs

E

E

Strength is affected by alloying,

heat treating, and manufacturing

process but stiffness (Modulus of

Elasticity) is not.



Elastic vs. Plastic Behavior

If the strain disappears when the

stress is removed, the material is

said to behave elastically.

When the strain does not return

to zero after the stress is

removed, the material is said tobehaveplastically.

The largest stress for which this

occurs is called the elastic limit.



Fatigue

Fatigue properties are shown onS-N diagrams.

When the stress is reduced below

the endurance limit, fatiguefailures do not occur for any

number of cycles.

A member may fail due tofatigue

at stress levels significantly below

the ultimate strength if subjected

to many loading cycles.



Deformations Under Axial Loading

AE

P

EE

From Hookes Law:

From the definition of strain:

L

Equating and solving for the deformation,

AE

PL

With variations in loading, cross-section ormaterial properties,

i ii

ii

EA

LP



221

21

in9.0

in.12

AA

LL

23

3

in3.0

in.16

A

L

Apply free-body analysis to each

component to determine internal forces,

lb1030

lb1015

lb1060

33

32

31

P

P

P

Evaluate total deflection,

in.109.75

3.0

161030

9.0

121015

9.0

121060

1029

1

1

3

333

6

3

33

2

22

1

11

A

LP

A

LP

A

LP

EEA

LP

i ii

ii

in.109.753

in.618.0in.07.1

psi1029 6

dD

EDetermine the deformation of the

steel rod shown under given loads.
http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/


13/29GIK Institute of Engineering Sciences and Technology.

Stresses in Vessels



Stresses in Vessels

Membrane stress pattern is totally changed for any variation in geometry as shown

in Figure above, i.e.

At Nozzle-cylinder

Flat End of Cylinder

Sphere-cylinder



Factor of Safety

stressallowablestressultimate

safetyofFactor

all

u

FS

FS

Structural members or machines

must be designed such that theworking stresses are less than the

ultimate strength of the material.

Factor of safety considerations:

uncertainty in material properties

uncertainty of loadings

uncertainty of analyses

number of loading cycles

types of failure

maintenance requirements and

deterioration effects

importance of member to structures

integrity

risk to life and property

influence on machine function



Stresses in Thin-Walled Pressure Vessels

Cylindrical vessel with principal stresses

1 = hoop stress

2 = longitudinal stress

t

pr

xrpxtFz

1

1 220

Hoop stress:

21

2

22

2

2

20

t

pr

rprtFx

Longitudinal stress:
http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/http://contents.ppt/




PointsA andB correspond to hoop stress, 1,

and longitudinal stress, 2

Maximum in-plane shearing stress:

t

pr

42

12)planeinmax(

Maximum out-of-plane shearing stress

corresponds to a 45o rotation of the plane

stress element around a longitudinal axis

t

pr

22max




Spherical pressure vessel:

t

pr

221

Mohrs circle for in-plane

transformations reduces to a point

0

constant

plane)-max(in

21

Maximum out-of-plane shearing

stress

t

pr

412

1max



Stresses in Vessels

Stresses in

Cylindrical Vessel

Stresses in Spherical Vessel

Stresses in Thick

Cylinders

Hoop Stress =

Axial stress =

Hoop = Axial =



Basic concepts for stress analysis

Equilibrium: external and internal

loading

Strain displacement compatibility

Constitutive relationships (for

material behavior, v,E)



Stresses in Vessels


25/29


Stresses in Vessels


26/29


Stresses in Vessels


27/29


Stresses in Vessels


28/29


Stresses in Vessels


29/29

Stresses in Vessels

Date post:	06-Apr-2018
Category:	Documents
Upload:	husnain-sikandar
View:	229 times
Download:	3 times

Lecture-02 Introduction to Shearing, Bearing and Maximum Stresses

Documents