Mechanics of solids

1. Mechanics of Solids (NME-302) Assignment:2
Yatin Kumar Singh Page 1
Problems in Economic Sections
Q: 1 A 10-m beam simply supported at the ends carries a uniformly
distributed load of 16 kN/m over its entire length. What is the
lightest W shape beam that will not exceed a flexural stress of 120
MPa? What is the actual maximum stress in the beam selected?
Q:2 Repeat Prob. 1 if the distributed load is 12 kN/m and the length
of the beam is 8 m.
Q:3 A 15-ft beam simply supported at the ends carries a
concentrated load of 9000 lb at mid-span. Select the lightest S
section that can be employed using an allowable stress of 18 ksi.
What is the actual maximum stress in the beam selected?
Q:3 A beam simply supported at the ends of a 25-ft span carries a
uniformly distributed load of 1000 lb/ft over its entire length.
Select the lightest S section that can be used if the allowable stress
is 20 ksi. What is the actual maximum stress in the beam selected?
Q:4 A beam simply supported on a 36-ft span carries a uniformly
distributed load of 2000 lb/ft over the middle 18 ft. Using an
allowable stress of 20 ksi, determine the lightest suitable W shape
beam. What is the actual maximum stress in the selected beam?
Q:5 A simply supported beam 24 ft long carries a uniformly
distributed load of 2000 lb/ft over its entire length and a
concentrated load of 12 kips at 8 ft from left end. If the allowable
stress is 18 ksi, select the lightest suitable W shape. What is the
actual maximum stress in the selected beam?
Q:6 A simply supported beam 10 m long carries a uniformly
distributed load of 20 kN/m over its entire length and a
concentrated load of 40 kN at mid-span. If the allowable stress is
120 MPa, determine the lightest W shape beam that can be used.
Problems in Unsymmetrical Beams
Q:1 The inverted T section of a 4-m simply supported beam has the
properties shown in Fig. The beam carries a uniformly distributed
load of intensity wo over its entire length. Determine wo if fbt ≤ 40
MPa and fbc ≤ 80 MPa.
Q:2 A beam with cross-section shown in Fig. is loaded in such a way
that the maximum moments are +1.0P lb·ft and -1.5P lb·ft, where P
is the applied load in pounds. Determine the maximum safe value
of P if the working stresses are 4 ksi in tension and 10 ksi in
compression.
Q:3 Find the maximum tensile and compressive flexure stresses for
the cantilever beam shown in Fig.
Q:4 A cantilever beam carries the force and couple shown in Fig.
Determine the maximum tensile and compressive bending stresses
developed in the beam.
Q:5 Determine the maximum tensile and compressive bending
stresses developed in the beam as shown in Fig.
Q:6
Determine the maximum tensile and compressive stresses
developed in the overhanging beam shown in Fig. The cross-section
is an inverted T with the given properties.
Q:7 A beam carries a concentrated load W and a total uniformly
distributed load of 4W as shown in Fig. What safe value of W can
be applied if fbc ≤ 100 MPa and fbt ≤ 60 MPa? Can a greater load be
applied if the section is inverted? Explain.
Q:8 A T beam supports the three concentrated loads shown in Fig.
Prove that the NA is 3.5 in. above the bottom and that INA = 97.0
in
4
. Then use these values to determine the maximum value of P so
that fbt ≤ 4 ksi and fbc ≤ 10 ksi.

2. Mechanics of Solids (NME-302) Assignment:2
Yatin Kumar Singh Page 2
Q:9 A cast-iron beam 10 m long and supported as shown in Fig.
carries a uniformly distributed load of intensity wo (including its
own weight). The allowable stresses are fbt ≤ 20 MPa and fbc ≤ 80
MPa. Determine the maximum safe value of wo if x = 1.0 m