Problem 2.3-3 q 3 kN/m F = 7 kN ; L = 12 m A q L B F
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Determine the stress resultants N(x), V(x), M(x) and draw the diagrams of the stress resultants and calculate the extremal values. At first, consider all parameters (F, a, L, ...) as variables and fill in their actual values at the end of your calculation.
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- Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPaA spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.: A hollow, pressurized sphere having a radius r = 4.8 in, and wall thickness t = 0.4 in. is lowered into a lake (see figure). The compressed air in the tank is at a pressure of 24 psi (gage pressure when the tank: is out of the water). At what depth D0will the wall of the tank be subjected to a compressive stress of 90 psi?
- A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)A spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Calculate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is O.h Assume E = 4 MPa and v = 0,45.
- A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d(see figure). The valve is designed to release the steam when the pressure reaches the value Pmax If the natural length of the spring, is L and its stiffness is k, what should be the dimension ft of the valve? (Express your result as a formula for h.)Two separate cables AC and BC support a sign structure of weight W = 1575 lb attached to a building. The sign is also supported by a pin support at O and a lateral restraint in the '-direction at D. (a) Find the tension in each cable. Neglect the mass of the cables. (b) Find the average stress in each cable if the area of each cable is Ae= 0.471 in2.Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure).
- A steam engine cylinder has an effective diameter of 35 cm and the maximum steam pressure acting on the cylinder cover is 12.5 kg/cm2. Calculate the number of 2-cm diameter required to fixthe cylinder cover. Assume that the permissible stress in the bolts is 330 kg/cm2.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)!As shown, three steel wires, each 28 mm2 in area, are used to lift a mass M. Their unstretched lengths are 19.99 m, 19.98 m, and 20 m. If M= 1,182 kg. what stress exists in the MIDDLE wire? Use E=215 Gpa. Answer must be in MPa.