재료역학7판07-03 Chap

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Problem 7.4-7 An element in pure shear is subjected to stresses

xy  3000 psi, as shown in the figure.
Using Mohr’s circle, determine (a) the stresses acting on an
element oriented at a counterclockwise angle   70° from the
x axis and (b) the principal stresses. Show all results on sketches
of properly oriented elements.
Solution 7.4-7 Pure shear
452 CHAPTER 7 Analysis of Stress and Strain
y
O x
3000 psi
x
0 y
0
xy
3000 psi
(a) ELEMENT AT 
70
(All stresses in psi)
2
140 
70 R
3000 psi
Origin O is at center of circle.
Point D:
Point D:
tx1y1
R sin 50
2298 psi
sx1
R cos 50
1928 psi
tx1y1
R sin 50
2298 psi
sx1
R cos 50
1928 psi
(b) PRINCIPAL STRESSES
Point P1:
1
R
3000 psi
Point P2:
2
R
3000 psi
up22up2
45
90
up12up1
45
90
D\'
D
A (
0)
3000 psi
2p1
2 =
140
P2 R P1
R
O
x1
B (
90)

x1y1
50
O x
2300 psi

70
1930 psi
1930 psi
y
D
D\'
O x
p1

45
3000 psi 3000 psi
y
P2
P1
Problem 7.4-8 An element in pure shear is subjected to stresses

xy16 MPa, as shown in the figure.
Using Mohr’s circle, determine (a) the stresses acting on an element
oriented at a counterclockwise angle   20° from the x axis and (b)
the principal stresses. Show all results on sketches of properly oriented
elements.
y
O x
16 MPa

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재료,   역학,   재료역학,   재료역학7판07-03 Chap