A bar with varying cross section is subjected to various forces as shown below. Compute: a) Stresses in each section b) strain in each section c) total extension of the bar. Take E = 2.1x105 N/mm² 400 mm² P1=10kN A 1000 mm B 800 mm mm² P₂ P3=45KN+ 1500 mm 600 mm² 800 mm → P4-35kN
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- An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
- The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.The Poisson ratio formula for an auxetic structure given in the figure is given as follows:H = 8 cm L = 4 cm α = 50 ° t = 5 mmThe strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition:a) Calculate the strain on the Z axis of the structure.b) In this case, what is the strain type of the structure in the Z axis?A bar with varying cross section is subjected to various forces as shown below. Compute: a) Stresses in each section b) strain in each section c) total extension of the bar. Take E = 2.1x105 N/mm² P1=17 kN P3=38 kN P4-21 KN 400 mm P₁+ A 1000 mm B 800 mm² P2 P3+ 1500 mm 600 mm² 800 mm P4
- The Poisson ratio formula for an auxetic structure given in the figure is given as follows: H = 8 cm L = 4 cm α = 50 ° t = 5 mm The strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition: a) Calculate the strain on the Z axis of the structure. b) In this case, what is the strain type of the structure in the Z axis?FF2 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 section
- At a point in an elastic material under strain, the stresses on the three mutually perpendicular planes are as follows:A normal tensile stress of 60 N/mm^2and shear stress of 40 N/mm2 on one plane and a normal tensile force of 40 N/mm^2and a complimentary shear stress of 40 N/mm^2 on another plane. Find the following using Mohr circle only (take 5 N/mm2 = 1 cm)a. The principal stresses and principal planes.b. The maximum shear stress and its plane.c. The normal and shear stress on a plane inclined at an angle of 30Oto major principal plane.1.4-7 The data shown in the table below were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 13 mm and a gage length of 50 mm (see figure for Prob. 1.4-3). At fracture, the elongation between the gage marks was 3.0 mm and the minimum diameter was 10.7 mm. Plot the conventional stress-strain curve for the steefor the steel and determine the proportional limit, modulus of elastics of elastic- ity (i.e., the slope of the initial part of the stress-strain,tress-strain curve), yield stress at 0.1% offset, ultimate stress, percent, elongation in 50 mm, and percent reduction in area. 'ess, percent area. TENSILE-TEST DATA FOR PROB. 1.4-7 Elongation (mm) 0.005 0.015 0.048 Load (kN) 5 10 30 50 0.084 60 0.099 64.5 0.109 67.0 0.119 68.0 0.137 69.0 0.160 70.0 0.229 72.0 0.259 76.0 0.330 84.0 0.584 92.0 0.853 100.0 1.288 112.0 2.814 113.0 FractureThe horizontal member ABC supports a point load of P (KN) and is pin-supported at B and C. The member (link) DB is a structural steel that pin- supported at D with the given dimensions (All the pins will have 5mm diameter). a) If the force P=100 kN find the max shear stress in the pins. b) Find the max force P such that the member BD will remain elastic c) Find the max displacement of point A such #remain elastic