strength of materials outline overview axially loaded members thin-walled cylinder general state of...

Strength of Materials Outline Overview

• AXIALLY LOADED MEMBERS• THIN-WALLED CYLINDER• GENERAL STATE OF STRESS• PLANE STRESS + MOHR’S CIRCLE• PLANE STRAIN + MOHR’S CIRCLE• HOOKE’S LAW• TORSION• BEAMS• COMBINED STRESS• COLUMNS (BUCKLING LOAD)

Copyright Kaplan AEC Education 2008-2011


AXIALLY LOADED MEMBERS

• Modulus of Elasticity

• Poisson’s Ratio

• Thermal Deformations

• Variable Load

E

lateral strain

longitudinal strain

t oL t t



THIN-WALLED CYLINDER

GENERAL STATE OF STRESS

PLANE STRESS• Mohr’s Circle—Stress

STRAIN• Plane Strain

t

pr

t

2a

pr

t



HOOKE’S LAW

TORSION• Circular Shafts• Hollow, Thin-Walled Shafts

1

1

1

x x y z

y y x z

z z x y

E

E

E

TL

GJ

z

TL TGr rGJ J 2z

m

T

A t

1

1

1

x x y

y y x

z x y

E

E

E

xyxy

yzyz

xzxz

G

G

G

2

1 0

1 01

10 0

2

x x

y y

xy xy

E

2(1 )

E G

EG



BEAMS• Shear and Moment Diagrams• Stresses in Beams• Shear Stress• Deflection of Beams• Fourth-Order Beam Equation• Superposition

( )

( )

dVx

dxdM

V xdx

x

yE

1 M

EI

x

My

I

max,min

Mc

I

xy

VQ

Ib

2

2

d yM EI EI

dx

3

3

d yV EI

dx

4

4

d yEIdx

( )

( )

EI M x dx

EI y M x dx dx



COMBINED STRESS

COLUMNS

2

2

2

2

2/

cr

crcr

EIP

KL

I r A

P E

A KL r

Example Problems


Shear-Moment Diagrams


Solution


Mohr’s Circle for Stress


Solution


Solution (continued)


Normal Strain


Solution


Mohr’s Circle for Strain


Solution


Hooke’s Law


Solution


Strain/Deformation


Solution


Angle of Twist


Solution


Shear Stresses in Bending


Solution


Beam Deflection—Integration Method


Solution



47

384

wL

EI


Beam Deflection—Superposition Method


Solution

27

6tip

PL

EI


Thin Walled Pressure Vessels


Solution


Euler Buckling of Columns


Solution

strength of materials outline overview axially loaded members thin-walled cylinder general state of...

Documents

copyright kaplan aec

solution slide

stress slide

straindeformation slide

bending slide

hookes law slide

normal strain slide

angle of twist slide