This document contains 9 questions related to mechanics of solids problems involving beams. The questions involve selecting beam sections based on allowable stresses, calculating maximum stresses in beams, and determining maximum loads beams can support. Beam cross sections include W, S, T, and inverted T shapes. Beams are subjected to uniformly distributed loads, concentrated loads, and combinations of loads. Calculations require determining maximum bending moments and stresses given beam properties, loads, and stress allowability criteria.

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