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**Course Title: Strength of Materials (CVE 202)**

Course Lecturer: Engr. F. M. Alayaki Civil Engineering Department, College of Engineering, University of Agriculture Abeokuta, Nigeria Course Unit: 2 Contact Time: 2 Hours Laboratory Time: 1 Hour

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Course Content Direct Stress: Hooke’s experiment. Axially loaded bar, Tensile and compressive stresses. Strain; tensile and compressive strains. Stress-stain curves for ductile and brittle materials. Modulus of elasticity. Mechanical properties of materials; elastic limits, proportional limit, yield points, ultimate strength. Modulus of toughness. Percentage reduction in areas. Percentage elongation.

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**Principal stress: Definition, deductions from Mohr’s circle**

Principal stress: Definition, deductions from Mohr’s circle. Mohr’s circle method of determining stress and strain. Working stress, proof stress, Poisson’s ratio, modulus of rigidity. Factors of safety. Lateral stresses and strains. Bars of varying cross sections compound bars under stress and strain. Temperature stresses.

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**Torsion: effects of torsion. Twisting moment**

Torsion: effects of torsion. Twisting moment. Polar second moments of area. Torsional shearing stresses and strain. Modulus of elasticity in shear. Angle of twist. Rupture. Shearing force and bending moments: Simply supported beam. Loading forces and moments in beams. Shear and moment equations. Shear force and bending moment diagrams.

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Typical Questions 1. The following data were recorded during a tensile steel test: Diameter of bar = 20mm Distance between gauge points = 200mm Elongation due to load of 50KN = 0.18 Load at yield point = 79KN Failing or ultimate load = 127KN Calculate in N/mm2 the stress at yield point, (b) the ultimate stress, (c) the modulus of elasticity of the steel 2. ( a ) Define the following terms: Component of Forces Resultant Equilibrant Moment of Forces Centroid of a Body ( b ) i Define the terms shear force and bending moment. ii What do you understand by the term ‘point of contraflexure’?

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**( c ) Using simple sketches show the following types of beams**

Simply supported beam with a point load. Simply supported beam with Uniformly Distributed Load (UDL). 3. Three separate members of steel, copper and brass are of identical dimensions and are equally loaded. Young’s moduli for the materials are: steel, 210,000N/mm2; copper, 100,000N/mm2; brass, 95,000N/mm2. If the steel member stretches 0.13mm, calculate the amount of elongation in the copper and brass members. 4. (a) Define the terms shear force and bending moment. (b) What do you understand by the term ‘point of contraflexure’? (c) Using simple sketches show the following types of beams Overhanging beam with UDL. Cantilever beam with point load at its end. Simply supported beam with uniformly varying load.

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5. A cantilever beam AB 1.5m long is loaded with a UDL of 2 KN/m and a point load of 3KN as shown in fig. 1. Draw the shear force and bending moment diagram for the cantilever beam. Indicate the positions and values of the following. Point of zero shear force. Maximum shear force. Maximum bending moment. 6 (a) Derive from first principle the formula for the moment of inertia of a rectangular section. (b) Determine the moment of inertia Ixx of the section shown in fig. 2. 7. Define stress, strain, and elasticity. Derive a relation between stress and strain of an elastic body. 8. Two wires, one of steel and the other of copper, are of the same length and are subjected to the same tension. If the diameter of the copper wire is 2mm, find the diameter of the steel wire, if they are elongated by the same amount. Take E for steel as 200 x 103 N/mm2 and that for copper as 100 x 103 N/mm2.

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**3 KN 2KN/m A B 0.25m 1.00m 0.25m Fig. 1 24mm 24mm 300mm Fig. 2 200mm**

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