A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young's modulus of the material varies linearly from E, to E, along the length of the rod, the normal stress developed at the section S-S is E₁₁ P - L/2- L -S -S E2 P
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- -26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. aSolve the preceding problem if the mass of the tailgate is MT— 11 kg and that of the crate is hic— 6S kg. Use dimensions H = 305 mm, L = 406 mm, dc= 460 mm, and dT= 350 mm. The cable cross-sectional area is At= 11.0 mm'. (a) Find the tensile Force T and normal stress T in each cable. (b) IF each cable elongatesSolve the preceding problem if the norm al and shear stresses acting on the element are sx = 2100 kPa, sy= 300 kPa, and txy= -560 kPa, and the seam is oriented at an angle of 22.5° to the clement.
- Plastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.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.At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement
- To draw the internal normal force diagram, it is important to determine the internal normal force at section A. For the problem given in the figure, determine the internal normal force (kip) at A. Take P, = 4.5 kip, P2 = 8 kip. 3.50 kip 1.75 kip P1 P2 A D Bl 3.50 kip 1.75 kip 18 in: +12 in. 16 in.-The principal plane stresses and associated strains in a plane at a point are s1 = 36 ksi, s2 = 16 ksi, P1 = 1.02(10-3), P2 = 0.180(10-3). Determine the modulus of elasticity and Poisson’s ratio3. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown below. If the Young's Modulus is 2.1 x 105 N/mm2. Determine (i) Stresses in each section, and; (ii) Total extension of the bar. Section 3 Section 2 Section 1 35000 N 35000 N 2 cm DIA 3 cm DIA 5 cm DIA k-20 cm- 25 cm -22 cm-
- F2 Q1) Axial displacement of point C in the system shown on the left is 0.01 cm. Find the maximum elongation of the bar and the maximum normal stress. A F1 A. GIVEN: F2 = 100 kN, (1 = 240 cm, €2= 160 cm, bi = 5 cm, bz=10 cm, h=5 cm, E=2.107 N/em², a=20 cm Note: neglect stress concentration. h bị b2 A-A section3. A homogeneous bar with a cross-sectional area of 400 mm² is attached to fixed supports as shown in the figure. It is subjected to lateral forces P₁ = 20 kN and P₂ = 50 kN. Determine the normal stress developed in segments AB and BC. Answer: OAB = 80.55 MPa A B D P₁ P₂ 0.60 m 1.20 m 0.90 m 4. The two vertical rods attached to the rigid bar are identical except for the length. The bar is pinned at O and initially horizontal when the 6000-lb was applied. Determine the normal force exerted by the two rods. The weight of the bar is negligible. Answer: PA = 4090.91 lb B A O 6 ft 4 ft 4 ft 4 ft 2 ft 6000 lbA bar of square cross-section is subjected to point loads of P1, P2, P3, and P4 as shown here. Find the magnitude of the force P3 necessary for the equilibrium, if P1= 130 kN, P2 = 230 kN & P4 = 180 kN. Also, determine the stresses in each section & the net change in the length of steel bar, where the respective side of a square and lengths are d1=55mm, L1=31 cm, d2 = 40mm, L2=38 cm, d3=55 mm & L3 =30 cm. Take E = 185 GPa. The force P3 to make it to equilibrium in kN is The Stress in section 1 in N/mm2 is The Stress in section 2 in N/mm2 is The Stress in section 3 in N/mm2 is and The total change in length in x10-3 mm is