208
6 Two-Dimensional Problems in Elasticity …
7 c m
10t
A
R
B
.
12cm
9cm
3cm
Y B
Section AB
Y A
Fig. 6.18 Loaded crane hook
M = P R cos 30
◦
i.e.,
M = 2000 × 6 × cos 30
◦
= 10,392 kg-cm
Component of P normal to CD is given by,
N = P cos 30
◦
= 2000 cos 30
◦
= 1732 kg.
Therefore, stress at
C = σ c =
N
A
+
M
AR
1 +
y A
m(R + y A )
=
−1732
8
+
10,392
8 × 6
1 +
(−2)
0.0397(6 − 2)
∴ σ c = −2726.7 kg/cm
2 (Compression)
Stress at
D = σ D =
N
A
+
M
AR
1 +
y B
m(R + y B )
=
−1732
8
+
10,392
8 × 6
1 +
2
0.0397(6 + 2)
Therefore, σ D = 1363.4 kg/cm
2 (Tension).
6 Two-Dimensional Problems in Elasticity …
7 c m
10t
A
R
B
.
12cm
9cm
3cm
Y B
Section AB
Y A
Fig. 6.18 Loaded crane hook
M = P R cos 30
◦
i.e.,
M = 2000 × 6 × cos 30
◦
= 10,392 kg-cm
Component of P normal to CD is given by,
N = P cos 30
◦
= 2000 cos 30
◦
= 1732 kg.
Therefore, stress at
C = σ c =
N
A
+
M
AR
1 +
y A
m(R + y A )
=
−1732
8
+
10,392
8 × 6
1 +
(−2)
0.0397(6 − 2)
∴ σ c = −2726.7 kg/cm
2 (Compression)
Stress at
D = σ D =
N
A
+
M
AR
1 +
y B
m(R + y B )
=
−1732
8
+
10,392
8 × 6
1 +
2
0.0397(6 + 2)
Therefore, σ D = 1363.4 kg/cm
2 (Tension).