MAC211
Tutorial 4
Double Integration Method of Beams
Recommended reading:
Benham, P.P., Crawford, R.J. and Armstrong, C.G., Mechanics of Engineering Materials, Second
Edition, Longman, 1996, Chapter 7, pp. 185-207
Gere, J.M., Timoshenko, S.P., Mechanics of Materials, Third SI Edition, Chapman & Hall, 1991,
Sections 7.6, 7.2, 7.3, 7.5, 7.9.
Case, J. & Chilver, A.H., Ross, C.T.F., Strength of Materials and Structures, Third Edition, Edward
Arnold Ltd, 1993, Sections 13.1-13.15, 14.1-14.5.
1. Find the deflection at the mid-length of the beam shown below.
57wL4
12288EI
MAC211: Mechanics of Deformable Solids
M.J. Carré, R. Curry
2025
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MAC211: Tutorial 4
2. A horizontal beam of length L is fixed at one end and simply supported at the other. A
uniformly distributed load w/unit length extends from the fixed end to the mid-span.
Determine all the reactions and the deflection at the mid-span position.
13wL4
7wL 57wL
, 128 , y = 6144EI
128
MAC211: Mechanics of Deformable Solids
M.J. Carré, R. Curry
2025
Page 2 of 3
MAC211: Tutorial 4
3. A cantilever of length L and section modulus I, protrudes from a wall at a small angle
of β radians down from the horizontal. The cantilever supports a concentrated load W
at its mid-point and the free end rests on a prop such that the ends of the beam are
level. Derive an expression for the load carried by the prop.
+ 3EIβ
P = 5W
16
L2
MAC211: Mechanics of Deformable Solids
M.J. Carré, R. Curry
2025
Page 3 of 3