1. The document provides 10 examples of calculating bending stresses and permissible loads for different beam configurations. 2. The beams have various cross-sectional shapes, loads including uniform and concentrated loads, and span configurations such as simple, overhanging, and cantilevered. 3. The examples calculate quantities like maximum bending stress, required beam dimensions, and maximum permissible loads based on given allowable stresses.

1. EXERCISES ON BENDING OF BEAMS
1/
q A simple beam AB with span
length L = 3.5m carries a
h unifiorm load of intensity q =
L b 6.4 kN/m (see figure).
Calculate the maximum bending stress σ max due to the load q if the
beam has a rectangular cross section with width b = 140 mm and
height h = 240 mm.
Ans. σ max = 7.29 MPa
2/
A steel beam with over-
q = 115 kN/m hanging ends and wide-
flange cross section is
supported as shown in the
figure. The beam carries a
3m 6m 3m uniform load of intensity q =
115 kN/m on each overhang.
Assuming that the section modulus of the cross sectional area is A =
6.78x106 mm2, determine the maximum bending stress σ max in the
beam due to the load q.
Ans. σ max = 76.3 MPa
3/
A simple beam AB of span
length L = 7m is subjected to
P d P two wheel loads acting at
distance d = 1.5 m apart
A B (see figure). Each wheel
transmits a load P = 14 kN,
L and the carriage may occupy
any position on the beam.
Determine the maximum bending stress σ max due to the wheel loads if
the beam is an I-beam having sections modulus W = 265x103 mm3.
Ans. σ max = 147.4 MPa
4/
b A rectangular wood beam is to be cut from a
circular log of diameter d (see figure). What
should be the dimensions b and h in order
x h d that the beam will resist the largest possible
bending moment?
Ans: b = d / 3; h = d 2/3
5/ y

2. A wood beam ABC of square
q = 1.5 kN/ cross section is supported at A
m b and B and has an overhang
b BC (see figure). A uniform
L = L = load of intensity q = 1.5 kN/m
2.5m 2.5m acts on the beam.
Calculate the required side dimension b of the square cross section
assuming L = 2.5 m and σ allow = 12 MPa. Include the the effect of the
weight of the beam and assume the specific weight of the wood is γ
= 5.5 kN/m3.
Ans. =
: b 136 m m
6/
b A beam having a cross section in the
form of an unsymmetric I section (see
40 mm figure) is subjected to a bending
30 mm moment acting about the x axis.
300 mm Determine the the width b of the top
x flange in order that the stresses at the
top and bottom of the beam will be in
40 mm the ratio 4:3, respectively.
y
Ans. 400 mm m
: b
= 259 m
7/ q 450 mm 30 mm
A simple beam AB supports
A B a uniform load q that
L = 14m
includes the weight of the
beam (see figure).
1800 mm Determine the maximum
permissible load q based
upon: (a) σ allow = 110 MPa,
and (b) τ allow = 50 MPa
Ans.: (a)
q = 144 kN/m; (b) =
q 174 kN/m
30 mm
8/
A laminated wood beam is built up by gluing
50 mm together three 50 mm x 100 mm boards
(actual dimensions) to form a solid beam 100
50 mm mm x 150 mm, as shown in the figure. The
allowable shear stress in the glued joints is
50 mm
0.35 MPa and the allowable bending stress is
100 mm
11 MPa. If the beam is 1m long cantiliver,
what is the allowable load P at the free end?
(Disregard the weight of the beam)
Ans.: P
= 3.94 kN
9/
A steel beam ABC with an overhang BC is subjected to two
concentrated load P as shown in the figure. Compute the maximum
36
value of P, if the allowable normal stress is 160 MPa.
P P
3
A B
C 30
3
600 600 300
9 3

3. Ans.: P max = 530 N
10/
Two metric rolled-steel channels
are to be welded back to back and
used to support the loading
shown. Knowing that the allowable
normal stress for the steel used is
190 MPa, determine the most
economical channels that can be
used.
Ans.: C
230x22