Engineering Tutorials

1. Three vertical wires in the same place are suspended from a horizontal support. They are all of the same length and carry a load by means of a rigid cross bar at their lower ends. One of the wires is of copper and the two other are of steel. The load is increased and temperature changed so that the stress in each wire is increased by 10 N/mm². Find the change of temperature. E_s =205,000 N/mm², E_c = 102,000 N/mm², α_s = 11 x 10^-6/^oC, α_c = 18 x 10^-6/^oC.

2. Draw and describe Mohr’s circle. If, at a point in a material, the minimum and maximum principal stresses are 30 N/mm² and 90 N/mm², both tensile, find the shear stress and normal stress on a plane through this point making an angle of tan^-1 0.25 with the plane on which maximum principal stress acts.

3. A beam ABC, 20 m long is simply supported at A and B, 15 m apart and carries a load of 18 kN at 6 m from inclined at 60^o towards A together with a distributed load which is increasingly linear from zero at 10 kN/m at B. Draw the SF and BM diagram and calculate the magnitude and location of the maximum bending moment.

4. Derive the relation for a circular shaft when subjected to torsion known as torsion equation and state clearly the assumptions made.

5. A beam of I-section 400 mm x 200 mm has a web and flange thickness 20 mm, Calculate the maximum intensity of the shear stress across this section and sketch the shear stress distribution across the section of the beam, if it carries a shearing force of 300 kN at a section.

6. A fixed beam of 3 m span carries two point loads of 10kN each at a distance of 1m and 2m from the left support. Draw shear Force and Bending moment Diagrams and Find its central deflection. Take EI = 1200 kNm².

7. Compare the crippling load given by Euler’s and Rankine’s formula for a tubular steel strut 2.3 m long having outer and inner diameter of 38mm and 33mm, loaded through pin joints at both ends. Take the yield stress as 320 N/mm² and Rankine constant as 1/7500, E=200,000 N/mm². For what length of strut does the Euler formula ceases to apply.

8. What is moment area method? Where is it conveniently used? Find an expression for slope and deflection at any section of a simply supported beam with an eccentric point load, using this method.

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