mohr’s circle - principal strains
TRANSCRIPT
RAJESH KUMAR.B
The Problem
An element in a stressed material has tensile strain of 0.00025 and a compressive strain of 0.000125 acting on two mutually perpendicular planes and equal shear strains of 0.0001 on these planes. Find principal strains and position of the principal planes.
Step 1 Using a suitable scale, measure OL = = + 0.00025 xe
Y
L
xe = 0.00025
O
X
ye = 0.000125
Step 2 Using a suitable scale, measure OM = = - 0.000125 ye
Y
L
X
M
Take in negative sideye
O
xe = 0.00025
Step 3
Y
L
X
M O
ye = 0.000125 xe = 0.00025
T
2
es
2
es
At L , draw LT perpendicular to OX and equal to = 0.00005 in the downward direction
Step 4
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
2
es
At M , draw MS perpendicular to OX and equal to = 0.00005 in the upward direction
S
2
es
Step 5
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
S
2
es
Join ST to cut the line OX, at a point N .
N
Step 6
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
S
2
es
N
With N as centre and NS or NT as radius, draw a circle
Mark U and V at the points where the circle meets OX
Mohr’s Circle
U
V
Step 7
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
S
2
es
N
U
V
From N , draw a perpendicular to meet the circle at Z
Z
Step 7
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
S
2
es
N
U
V
Z
Find the VNT = and UNT =
12θ
12θ 22θ
22θ
Step 8
Y
L
XM
O
ye = 0.000125 xe = 0.00025
T
2
es
S
2
es
N
U
V
Z
12θ
22θ
NZemax
OV 1 e
OU 2 e
2e 1e