The figure below are 3 solid cylindrical bars joined together by a flange. Find the axial stress of each bars.
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- Two steel rods are welded together (see figure): the seam is oriented at angle ? = 50°. The stresses on the rotated element are sx1=10 ksi, sy1= -12 ksi, and tx1y1= -5 ksi. Find the state of plane stress on the clement if it is rotated clockwise to align the x3 axis with the longitudinal axis of the rods.A single steel strut AB with a diameter (a) Find the strut force Fs and average normal stress ds= 8 mm supports the vehicle engine hood of a in the strut. mass 20 kg that pivots about hinges at C and D (see (b) Find the average shear stress t aver in the bolt at A,figure parts a and b). The strut is bent into a loop at (C) Find the average bearing stress bon the bolt at A. its end and then attached to a bolt at A with a diameter db= 10 mm. Strut AB lies in a vertical plane.A post AB supporting equipment in a laboratory is tapered uniformly throughout its height H (see figure). The cross sections of the post are square, with dimensions b × b at the top and 1.5b × 1.5b at the base. Derive a formula For the shortening 8 of the post due to the compressive load P acting at the top. (Assume that the angle of taper is small and disregard the weight of the post itself.)
- A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.Solve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure).
- A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m acting in the directions shown in the figure, Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure).A steel bar with a diameter d = 12 mm is subjected to a tensile load P = 9.5 kN (see figure). (a) What is the maximum normal stresser smax in the bar? (b) What is the maximum shear stress tmax? (c) Draw a stress element oriented at 45° to the axis of the bar and show all stresses acting on the faces of this element. (d) Repeat part (c) for a stress element oriented at 22.5° to the axis of the bar.
- An aluminum tube has inside diameter dx= 50 mm, shear modulus of elasticity G = 27 GPa, v = 0.33, and torque T = 4.0 kN · m. The allowable shear stress in the aluminum is 50 MPa, and the allowable normal strain is 900 X 10-6. Determine the required outside diameter d2 Re-compute the required outside diameter d2, if allowable normal stress is 62 MPa and allowable shear strain is 1.7 X 10-3.A horizontal rigid bar of weight If' = 72001b is supported by three slender circular rods that are equally spaced (see Figure)'. The two outer rods are made of aluminum (£-, = 10 X 10 psi) with diameter f/j = 0.4 in. and length Ly= 40 in. The inner rod is magnesium {F-, = 6.5 X 10* psi) with diameter rf, and length L-,. The allowable stresses in the aluminum and magnesium are 24,000 psi and 13,000 psi, respectively. IF it is desired to have all three rods loaded to their maximum allowable values, what should be the diameter d2and length LzoF the middle rod?A tubular bar with outside diameterd2= 4.0 in, is twisted by torques T = 70,0 kip-in. (see figure). Under the action of these torques, the maximum tensile stress in the bar is found to be 6400 psi. Determine the inside diameter rtf of the bar. If the bar has length L = 48.0 in. and is made of aluminum with shear modulus G = 4,0 × 106 psi, what is the angle of twist d (in degrees) between the ends of the bar? (c) Determine the maximum shear strain y (in radians)?