LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

MODULE 2

LOAD AND STRESS ANALYSIS

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS

Load

Equilibrium equations

Complex stresses

Stress transformation

Mohr’s circle

Stress-strain relations

Stress concentration

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

A branch of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces acting within the body.

Mechanics of Materials

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Applications involving combined loading

Typical Engineering Structures

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Types of Loading on Structures

LOAD SYMBOL UNITS(Metrics)

UNITS(Engineering)

Direct Force F, P N lbf

Shear Force V, Q N lbf

Torsion T Nm lbf-ft

Bending Moment M Nm lbf-ft

Fluid Pressure p Nm-2 psi

Temperature Difference

T oC oF

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Types of Loading on Structures

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Equilibrium of a Deformable Body

A body is said to be in equilibrium when the resultant of all forces and moments acting on the body is zero.

0

0

oM

F

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Under General Loading Conditions

Stress – intensity of a force acting at a material point

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Simple Stresses

J

Tr

A

P

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Complex Stresses

T

P•A

What is the magnitude of stress and strain on specific plane at A?

Does the stress and strain represent critical / maximum values at A?

If not… what is the maximum & minimum

(principal) stresses and maximum shear stresses?

What is the corresponding strain values? On which planes do these stresses act?

A

Shear stress

Normal stress

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Transformation Equations

2sin2cos22 xy

yxyxx

2cos2sin2 xy

yxyx

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Mohr’s Circle

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Fracture Planes

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Engineering Stress and Strain

P – applied force

Ao – original cross-sectional area

Lo – original gage length

L – instantaneous length

s =

P

Ao

e =

DL

Lo

= L - Lo

Lo

Engineering stress,

Engineering strain,

P

P

LLo

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Engineering Stress-strain Curve

e

So

PlasticElastic

s

Necking

Fractured

Fractured

Tensile failure in ductile material is associated with large plastic deformation.

eTotal = eel + epl

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

STRAIN,

0.0 0.1 0.2 0.3 0.4 0.5 0.6

ST

RE

SS

, (

MP

a)

0

200

400

600

800

STRAIN,

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

ST

RE

SS

, (

MP

a)

0

50

100

150

200

= E

Linear

Non-linear /Power-law

= E

= K(p)n

SS316 steel

Engineering Stress-strain Curve

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Mechanical Properties of Some Materials

MATERIALS E GPa (!06 psi)

So

MPa(ksi)

SU

MPa(ksi)

AISI 1040steel

207(30)

413(60)

620(90)

Stainless Steel 314

193(28)

205(30)

515(75)

7075Al alloy

72(10.5)

105(15)

230(33)

Gray cast iron

- - 152(22)

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Concentration

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Concentration

Stress concentration factor

avgtK

max

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Concentration

SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM

SME 4133 Failure of Engineering Components and Structures

Stress Concentration Factors

SKMM 4133 Failure of Engineering Components and Structures