Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 6 (Q.No. 12)
12.
A square beam and a circular beam have the same length, same allowable stress and the same bending moment. The ratio of weights of the square beam to the circular beam is
Discussion:
12 comments Page 2 of 2.
Moun said:
6 years ago
Thanks @Ankit.
Chinna said:
5 years ago
For square beam Z1 =a^3/6
For circular beam Z2=πd^3/32.
(Since having the same length, same allowable stress and same bending moment section modulus of both beam equals z1=z2).
(a^3)/6=π(d^3)/32
(d=1.193a) (d in terms of a).
(Weights of two beams proportional to cross-sectional areas )
W1/W2 =A1/A2 (area of square beam=a^2).
( Area of circular bean=πd^(2)by 4)
=( a^2)/π(d^2)/4 ( substitute d value )
= 1/1.118
W1/W2=1/1.12 (answer).
For circular beam Z2=πd^3/32.
(Since having the same length, same allowable stress and same bending moment section modulus of both beam equals z1=z2).
(a^3)/6=π(d^3)/32
(d=1.193a) (d in terms of a).
(Weights of two beams proportional to cross-sectional areas )
W1/W2 =A1/A2 (area of square beam=a^2).
( Area of circular bean=πd^(2)by 4)
=( a^2)/π(d^2)/4 ( substitute d value )
= 1/1.118
W1/W2=1/1.12 (answer).
(1)
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