Stress and Strain - Structural and Stress Analysis - page 183

PROBLEMS

P.7.1 A column 3m high has a hollow circular cross section of external diameter
300mm and carries an axial load of 5000 kN. If the stress in the column is limited
to 150N/mm 2 and the shortening of the column under load must not exceed 2mm
calculate the maximum allowable internal diameter. Take E

200 000N/mm 2 .

=

Ans . 205.6mm.

P.7.2 A steel girder is firmly attached to a wall at each end so that changes in its length
are prevented. If the girder is initially unstressed, calculate the stress induced in the
girder when it is subjected to a uniform temperature rise of 30 K. The coefficient of
linear expansion of the steel is 0.000 05/K and Young's modulus E 180 000N/mm 2 . =

(Note L = L 0 (1 + α T ).)

Ans . 270N/mm 2 (compression).

P.7.3 A column 3m high has a solid circular cross section and carries an axial load of
10 000 kN. If the direct stress in the column is limited to 150N/mm 2 determine the
minimum allowable diameter. Calculate also the shortening of the column due to this
load and the increase in its diameter. Take E 200 000N/mm 2 and ν = = 0 . 3.

Ans . 291.3mm, 2.25mm, 0.066mm.

P.7.4 A structural member, 2m long, is found to be 1.5mm short when positioned
in a framework. To enable the member to be fitted it is heated uniformly along its
length. Determine the necessary temperature rise. Calculate also the residual stress
in the member when it cools to its original temperature if movement of the ends of
the member is prevented.

If the member has a rectangular cross section, determine the percentage change
in cross-sectional area when the member is fixed in position and at its original
temperature.

200 000N/mm 2 , Poisson's ratio ν Young's modulus E 0 . 3 and the coefficient of

linear expansion of the material of the member is 0.000 012/K.

= =

Ans . 62.5 K, 150N/mm 2 (tension), 0.045% (reduction).

P.7.5 A member of a framework is required to carry an axial tensile load of 100 kN. It
is proposed that the member be comprised of two angle sections back to back in which
one 18mm diameter hole is allowed per angle for connections. If the allowable stress
is 155N/mm 2 , suggest suitable angles.

645 . 2mm 2 . From steel tables, two

Ans . Required minimum area of cross section =

equal angles 50 × 50 × 5mm are satisfactory.