A pipe with an outside diameter of 216 mm and a wall thickne

A pipe with an outside diameter of 216 mm and a wall thickness of 7 mm is subjected to the 19 kN load shown in Figure P15.54/55. The internal pressure in the pipe is 2.0 MPa. Assume that the pipe has closed ends. Determine the normal and shear stresses on the top surface of the pipe at point H. the principal stresses and maximum in-plane shear stress at point H and show the orientation of these stresses on an appropriate sketch. The absolute maximum shear at H.

Solution

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Resove the 19kN force into two components vertical and horizontal.

Both produce bending moment about H, however the moment due to horizontal component will not produce any bending stress at H, as H is on the neutral axis.

The vertical component will produce a bending moment and torque about H

F_v = 19x1000xsin55 = 15564 N-m.

bending moment M = 15664 x 0.75 = 11673 N-m.

Bending stress = My / I = 50.2 n/mm²

The pressure inside the pipe produces longidudinal stress = pd/4t = 2.4x202 / 4x7 = 17.3 N/mm²

and circumferential stress = pd/2t = 2.4x202 / 2x7 = 34.6 N/mm²

Total stress in longitudinal direction = 50.2 + 17.3 = 67.5 N/mm²

Stress in circumferential direction = 34.6 N/mm²

F_v also produces a torque T =15564 x 1.25 = 19455 N-m

Shear stress due to torque = Tr / J = 167.4 N/mm²

At H two normal stresses 34.6 and 67.5 N/mm² both perpendicular to each other and a shear stress 167.4 N/mm²

Max principal stress = 219.25 N/mm²

Min. principal stress = -117.15 N/mm²

Max shear stress = 168.2 n/mm²