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6.1.1 Plates. A plate is a flat structural element for which the thickness is small compared with the surface dimensions. The thickness is usually constant but may be variable and is measured normal to the middle surface of the plate, Fig. 6.1.1. lateral load.
Simple Stresses. Thin-walled Pressure Vessels. A tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections. TANGENTIAL STRESS, σt (Circumferential Stress) Consider the tank shown being subjected to an internal pressure p.
The angular deflection of a torsion hollow shaft can be expressed as α = 32 L T / (G π (D 4 - d 4 )) (5b) The angle in degrees can be achieved by multiplying the angle θ in radians with 180 / π.
Geometry. Radius is at least 10 times the wall thickness. Deformation. The strain varies insignificantly across the wall thickness. The walls are in a state of “plane stress” Material behavior. Linear elastic, small deformations (like usual) Stresses in cylindrical pressure vessels.
Stress in Radial Direction. The stress in radial direction at a point in the tube or cylinder wall can be expressed as: σr= [ (pi ri2 - po ro2) / (ro2 - ri2)] - [ri2 ro2 (po - pi) / (r2 (ro2 - ri2))] (3) maximum stress when r = ri (outside pipe or cylinder)
itsnormalpointsinthe+ydirection. Theverticalplaneontherightisa+xplane. Similarly, theleftverticalandlowerhorizontalplanesare −yand−x,respectively.
Water enters a cylindrical tank with diameter, D, through two pipes at volumetric flow rates of Q1 and Q2 and leaves through a pipe with area, A 3 , with an average velocity, . The level in the tank, h , does notV
