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Axial - Problem#1(60 points A rigid bar BCD is attached to...

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Unformatted text preview: Problem #1 (60 points) A rigid bar BCD is attached to a horizontal 1 in. diameter aluminum rod at B and is pinned at C. When a vertical 5 kip load is applied at D, determine: a) the normal stress in the aluminum rod AB; b) the vertical displacement of point D (assuming side BC is initially vertical and side CD is initially horizontal); c) the average shear stress in the 3A in. diameter aluminum pin at C. Rod materials properties: E = 10 x 106 psi, G = 4.26 x 106 psi, v-= 0.17, a = 12.8 x 10'6 / 0F ' A rod 1 in. diam 8. Problem 1 (90 points) The rigid bar ABCD of negligible weight is initially horizontal at a temperature of 40 0 F, and the steel rods attached at A and C are stress-free. Determine the stress in each rod after a force of F = 30 kips is applied at D and the temperature changes to 90 0 F. The rod attached at A has a length of 6 fl and a cross-sectional area of 0.8 inz. The rod attached at C has a length of 4 ft and a cross-sectional area of 0.5 inz. The rigid bar has dimensions of a = 5 ft, b = 2 ft, and c = 1 ft. NOTE: Just set up the equations with known numbers inserted until you have a clearly solvable system (2 equations in 2 unknowns) but do not spend time solving for the numerical answer. Circle these equations and explain-what you would do with the numerical result of this system to obtain the answers requested. We’re grading on the logic of your solution, not the numerical answer, so be sure your work is neat and organized. Problem 2 (50 points) A 60 in. x 72 in. bundle is wrapped by a 1 in. wide by 1/16 in. thick reinforced plastic band under 400 1b tension. Given the material property data below, determine the: a) axial stress in the band, l,_ . ' ____.| b) elastic elongation of the band, 72 m c) final width ofthe band (considering '7 0‘ T an only the effect caused by the axial stress) I 1 4 - d) temperature change (in degree F) B '6 w m necessary to relax all tension stress so that / _L the net elongation of the band is zero. Elastic Modulus = 1 x 106 psi, Poisson Ratio = 0.4, Thermal coefficient = 9.0 x 10‘5 / 0F Problem #2 (60 points) The support beam shown 15 rigidly fixed between the floor and the ceiling and IS initially stress- free. Determine the maximum normal stress in the beam when a load pf P— — 10 kN 15 applied at C and the temperature is raised by 12 0C. Indicate which section of the beam experiences this stress and whether the stress is tensile or compressive. Beam materials properties: E = 70 GPa, G = 30 GPa, v = 0.17, on = 23.1 x 106/ 0C3 Form # Problem #2 (70 points) The rigid bar ABC is supported by a pin at A and a 9 ft composite cable at C. The composite cable has a cross-sectional area of 0.250 in 2. The upper third of the composite cable is made of magnesium and the lower two thirds of the cable is made of bronze. a) If the force of P = 2000 lb is applied at B, determine the displacement of points B and C. Material E (psi) Magnesium 7.0x10 6 Bronze 15.0x10 6 b) Briefly describe Saint-Venant’s Principle 550$ El A rigid platfonn weighing 2000 lbs is hinged at point A and supported by a 6 ft long 1/2 inch diameter steel rod at point B and a 12 ft long V2 inch diameter steel rod at point C. Before the platform is attached to the rods, the rod ends B and C are horizontally in line with the pin at point A. Once the platform is attached to the rods and the two loads shown in the figure are placed on the platform, find a) the normal stress in rod BD, b) the normal stress in rod CE, 0) the displacement of point C. Material Properties: E=30x106psi,G= 11x 10"psi,v=o.32,a= 6.6x lot/OF (1) Without plugging in numbers, write the new compatibility equation for this problem if rod CE experiences a temperate drop of AT while the rigid platform is attached to the rods. 2. A 4-ft concrete post is reinforced by four steel bars, each of 3A-in. diameter. Knowing . that ES = 29 x 106 psi, as = 6.5 x 10'6/°F and E = 3.6 x 1.06 psi, ac = 5.5 x 10‘/°F, determine: (a) (25 points) the normal stresses induced in the steel and in the concrete by a temperature rise of 80°F; (b) (10 points) the changes in dimensions of a diameter of the steel bar if I); = 0.3 4ft 8 in. Answers: (3) cs = 0'c = (b) d'= SPOZV 5pon 1. The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500mm2; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600mm2. For the 30-kN force shown, determine: (a) (15 points) the normal stresses in links AB and CD; (b) (5 points) the average shear stress in 24-mm-diameter pin D if the pin is in double shear. (c) (15 points) the vertical displacement at point B; Answers: (a) CAB = 0CD = (13) TD = (C) AB = Form # Problem #3 (65 points) A 6061 — T6 aluminum rod is inserted through a hole in a rigid, fixed plate m and pinned in place, as shown in the figure at a temperature of 80 0 F. The space between the rod’s rigid end cap and the plate is 0.01 in. a) Determine the axial stress in the bar when the temperature drops to 20 0 F. A - [.5 2.." (Neglect the thickness of the rigid plate and assume the end cap at the bottom of the rod is also rigid.) b) Is the rod in tension or compression? 0) What is the total strain in the rod at 20 0 F? Form # _ Problem #2 (60 points) 50,000 lb The 2 in. diameter, 2 1/2 ft long aluminum rod supports a 50,000 lb axial load as shown. For support, the lower 1 1/2 ft section is attached to a steel sleeve having an inner diameter of 2 in. and an outer diameter of 3 in. a) For segment BC, determine the average normal stress in each material. Aluminum Steel b) Calculate the vertical displacement of the free end at A. Modulus of Modulus of Yield Strength (ksi) Coef. of Them. Material Elasticity E Rigidity G 0'y Poisson’s Expansion 0L ( 103 ) ksi ( 103 ) ksi Tens. Comp. Shear Ratio ( 10'6) / 0F 10.0 3.7 37 37 19 0.35 13.1 29.0 . 36 36 . 6.6 5603 E! ...
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