Determine the distribution of shear force, bending moment and stress due to bending in simply supported beams

Q1: Determine distribution of shear force, bending moment and stress due to bending in the simply supported beam shown in the figure below, the beam self-weight is included in the uniformly distributed load.

180mm

90 kN 35 kN

UDL 4.2 kN/m

420mm 25mm

35mm

3.2m 4.8m 1.6m

Sketch graphs of shear force and bending moment distribution and validation of calculations by alternative checking methods, plus analysis of safety factor for a chosen material, incorporating referenced additional data, are required for M/D criteria.

Task 2 – Learning Outcome 1.2

Select standard rolled steel sections for beams and columns to satisfy given specifications

Q1: Select a standard rolled steel I-section for the simply supported beam shown in figure below. Select an appropriate factor of safety and material strength. Include references for all source information employed. The self-weight of the beam itself may be neglected when calculating the maximum moment.

60 kN 6.4 kN/m

2.8 m 2.8 m

Justification, with references, for choice of steel grade and factor of safety required, plus incorporation of material selfweight into analysis required for M/D criteria.

Q2: A column is made from a universal I-section 203 x 203 x 60. A load of 96 kN is applied on the y-axis offset 50mm from the centroid. Calculate the stress at the outer edges of the y-axis and comment on the overall stresses on the column.

y

Task 3 – Learning Outcome 1.3

Determine the distribution of shear stress and the angular deflection due to torsion in circular shafts

Q1: A hollow circular shaft has an internal diameter of 48 mm and an external diameter of 54 mm. Calculate the shear stress produced at the outer and inner surfaces of the shaft when the applied torque is 128Nm; comment on your results.

Q2: The transmission output shaft for a heavy goods vehicle can withstand a safe working shear stress of 54MPa. Its outside diameter is 54mm and its internal diameter is 48mm. Calculate the maximum power which can be transmitted by the shaft at 3600rpm.

Q3: Calculate the angular deflection (in degrees) produced in a solid circular shaft of diameter 12.5 mm and length 0.5 m when the shear stress is 25MPa and the shear modulus 70GPa. What torque would be required to achieve this?

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