A rubber ball (see figure) is inflated to a pressureof 65 kPa. At that pressure, the diameter of theball is 240 mm and the wall thickness is 1.25 mm. Therubber has a modulus of elasticity E = 3.7 MPa andPoisson’s ratio v = 0.48.(a) Determine the maximum stress and strain inthe ball.(b) If the strain must be limited to 0.425, find theminimum required wall thickness of the ball.

The ring, with dimensions shown, is placed over a flexible membrane which is pumped up with a pressure p. The thickness r,-r; is small compared to r; (a) Determine the axial force F in the ring in terms of p, w and r;. Hint: Consider a FBD by cutting the ring+membrane in two. (b) Determine the hoop stress in the ring. (c) Determine the hoop strain in the ring. The modulus of elasticity for the ring is E. (d) Relate the hoop strain to the change in the inner radius of the ring after this pressure is applied, and use this to get the change in the inner radius in terms of p, E, w, r, and ri- (PLEASE ANSWER ASAP AND CORRECTLY)!

The two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0, 0). After load P is applied, joint B moves to the coordinate position (0.20 in., -0.55 in.). Assume a = 9 ft, b = 6 ft, and h = 7 ft. Determine the normal strain in each bar. B P b h

A thin-walled cylindrical pressure vessel of inner radius r = 0.6 cm and a thickness of 0.06 cm is subjected simultaneously to internal gas pressure p = 3.5 MPa, a compressive force F = 800 N acting at the ends, and a torsional load of 25 N · m (see figure). Determine the following quantities (a) the principal stresses at a point H on the surface of the vessel and the absolute maximum shear stress; (b) the normal strain along x-axis (ɛx) and the shear strain (yxy) at the same point H. See the established Oxy coordinate system. The Young's modulus of the material is 200 GPa and the Poisson's ratio is 0.3. Hint: the cross-section of the vessel can be regarded as a hollow tube and the cross-section area can be calculated as 1(0.00662 – 0.006²). You can do the same treatment for the polar moment inertia. 25 N· m F F H X 25 N· m

Athin rectangular polymer plate PQRS of width b = 429 mm and height a = 140 mm is shown in the figure. The plate is deformed so that corner Q is displaced upward by c = 1.6 mm and corner R is displaced leftward by the same amount. Determine the shear strain at corner P after deformation. a Y = y i b Q S a X urad

The stresses shown act at a point in a stressed body.  The stress magnitudes are Sx = 50 MPa and Sy = 250 MPa, acting in the directions indicated in the figure.  Using the equilibrium equation approach, determine the normal and shear stresses at this point on the inclined plane shown.  Assume β = 46°.

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