Strength of materials questions.

1. Derive the bending equation relating the loads and moments on a beam with its physical properties and dimensions stating clearly any assumptions of the theory of bending.
2. In a construction site, a hollow circular bar with its outside diameter being twice the inside diameter is used as a beam. From the bending moment diagram of the beam it is found that the bar is subjected to a bending moment of 40 kNm. Determine the inside diameter of the bar if the allowable bending stress is to be limited to 100 Mpa.

1. Derive the general twisting formula linking the torque(T) with the shear stress and other physical parameters of a hollow shaft of length l and internal and external diameters of d and D respectively.
2. In a sisal processing factory a hollow shaft with the ratio of internal to external diameter being equal to 3/8 is transmitting 600 kW power at a rotational speed of 110 rpm. The maximum torque is 20% greater than the mean torque while the shear stress is required not to exceed 63 Mpa. Also the angle of twist in a length of 3m is not to exceed 1.4 degrees and shear modulus of rigidity of the shaft material is given as 84 Gpa. Calculate the maximum external diameter of the shaft satisfying these conditions.

1. Determine the bursting pressure for a cold drawn seamless steel tubing of 0.06 m internal diameter with a wall thickness of 0.002 m given that the ultimate strength of steel is 380 MPa.
2. A cast-iron main pipe conveys water at pressure head of 100 m and has a diameter of 0.8 m. Calculate the thickness of the wall for the pipe given that the maximum permissible tensile stress is 20 MPa and specific gravity of water is 10KN/m³.

An axially loaded bar made of brass and steel has dimensions as shown in the figure below.

Two axial forces P1 and P2 are acting in the direction shown at points A and B respectively with P1=30 kN and P2= 15kN. The Modulus of Elasticity for steel and brass are given as 210 and 105 GPa respectively. Calculate

1. The maximum normal stress in the steel and brass sections
2. The displacement at the free end A

1. A horizontal beam ABCDEFG is loaded as shown in the figure below.

Calculate the reactions and forces acting at different points on the beam and draw the shearing force and bending moment diagrams.

2. A contilever beam which is 2m long is loaded with a point load of 1.4 kN at its free end and a uniformly distributed load of 3.4 kN per meter length running over 1.2 m from the fixed end. The cross section of the cantilever beam is rectangular with dimensions 80mm by 160mm and it is made of material with a modulus of elasticity of 10 GPa. Calculate the deflation at the free end.

A rectangular beam with cross sectional dimensions of 250mm (depth) and 150mm (width) is subjected to a maximum bending moment of 750kNm. UNder such loading determine

1. The maximu stress in the beam
2. The radius of curveture for that portion of the beam where the bending is maximum given the value of the Young`s Modulus of elasticity for the beam material is 200GPa.
3. The value of longitudinal stress at a distance of 65mm from the top surface of the beam.

A simply supported beam BCDF has the following dimensions: BC=15m, CD=15m, DF=30m. The beam carries a concetrated load of magnitude 200kN at point C and another one of magnitude 80kN at point D. In addition, there is a uniformly distributed load (UDL) of magnitude 10kN/m over the 30m length DF. The beam is simply supported at the point B and F and has a uniform cross section. Draw the shearing force and moment diagrams for this loading of the beam.

A horizontal beam of uniform cross sectional area is 6m long and is simply supported at its ends. Two vertical concentrated loads of magnitude 48kN and 40kN act at distances 1m and 3m respectively from the left end support. Given that E=200GPa and I=85x10^-6m⁴, determine the position and magnitude of the maximum deflection.

1. Explain the undestanding of statically indeterminate and statically determinate beams.
2. Define the Euler`s Formula for calculating the critical loads for a column or a strut stating any assumptions made in its derivation.
3. A solid round bar of 60mm diameter and 2.5m long is used as a strut. One end of the strut is fixed while its other end is hinged. Determine the safe compressive load for this strut using Euler`s formula Assume E=200GPa and the factor of safety=3.