SF & BM Diagrams, 2D Stress Analysis and Beam Deflection.

In a large scale manufacturing plant, a section of a steel pipe is supported over a span of 7 m between two flanges and may be considered to be simply-supported by pins at each end. The pipe has an outside diameter of 300 mm and a wall thickness of 15 mm. Due to the operating conditions (including external environment conditions such as temperature changes and also, supporting other structures), a concentrated load of magnitude 120 kN acts at the pipe section midspan perpendicular to the pipe axis, and a uniformly distributed load of magnitude 10 kN/m acts along the span of the pipe. In addition, a concentrated load of 75 kN acts at the right hand end perpendicular to the pipe axis and, an additional concentrated load of 50 kN also acts at the right hand end, inclinded at 45° to the pipe axis. The pipe is also subjected to a compressive axial force of 200 kN, and a force acting tangential to the pipe outside surface of magnitude 430 kN.

i) Draw the thrust, shear force and bending moment diagrams for the loaded pipe due to the loading, and determine the magnitude and position of the maximum bending moment. Highlight all other significant values.

ii) Determine the magnitude and the location of the maximum bending stress acting in the pipe material.

iii) Calculate the maximum tensile and compressive stresses acting in the pipe and show on a neat sketch how they are distributed through the pipe cross-section.

iv) Calculate the torsional shear stress acting in the pipe, and sketch the distribution through the pipe cross-section. Determine also the angle of twist of the pipe in degrees.

v) Determine the major and minor principal stresses and the maximum shear stress acting on the bottom surface of the pipe, and the angle on which the principal stress acts by an analytical and graphical method.

vi) Calculate the maximum deflection of the pipe due to the lateral loading using simple superposition and Macauley's method, and comment on the values obtained.

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