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- A steel bar 300 mm long and having 24 mm diameter, is turned uuwn to 18 mm diameter for one-third of its length. It is heated at 30°C above room temperature, clamped at both ends and then allowed to cool to room temperature. If the distance between the clamps is unchanged, the maximum stress in bar [a = 12.5 x 10/°C and E = 200 GN/m2] is Q.3When installed, bar AB had negligible axial stress. When the bar's temperature is 124°F the axial compressive stress is 14.4 ksi. The bar is made from a ductile metal which has the following properties: E=25x10° psi, a = 9.00x10 6 (h)/°F, and v = 0.29. Assume elastic behavior. ( in. in. В 50 in.- Determine: a. The thermal strain in the bar's axial (longitudinal) direction if it could expand freely: b. Temperature at which bar was installed: c. The total strain in the lateral direction:Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in.-long bronze [E = 15900 ksi, 9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x 10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48 a = %3D in., a=32 in., b=44 in., and c=14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand the temperature is decreased by 120°F, determine: (a) the normal stresses in bars (1) and (2). (b) the normal strains in bars (1) and (2). (c) the deflection of the rigid bar at point D. (2) L2 A B D L1 (1)
- Q1: An Iron bar has a length of 50 m when the temperature is (-20 "C) .what is the length of the bar in a summer day when the temperature is (38 C) ?Calculate the thermal stress set up in the bar on summer day.a=12 x10 C ,E=25x10 Pa.A horizontal bar, fixed at one end (x = 0), has a length of 1 m. and cross-sectional area of 100 mm2 Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, where is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 KN is applied at the free end (x = 1). The axial displacement of the free end is..... mma 20mm diameter bronze bar 3.4m long is place between two rigid walls. at a temperature of -31°C, the gap ∆= 4.7mm. Find the temperature (at degree Celsius) at which the compressive stress in the bar will be 39MPa . Use alpha = 19.59x10^-6 m/(m.°C) and E= 87GPa.
- A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L1. (A). A 25mm square cross-section bar of length 300mm carries an axial compressive load of 50kN. Determine the stress set up in the bar and its change of length when the load is applied. For the bar material E = 200 GN/m. [80 MN/m², 0.12mm] 2. (A). A steel tube, 25 mm outside diameter and 12mm inside diameter, cames an axial tensile load of 40 kN. What will be the stress in the bar? What further increase in load is possible if the stress in the bar is limited to 225 MN/m?? [106 MN/m²; 45 kN]A steel rod with a cross-sectional area of 0.25in .^ 2 is stretched between two fixed points. The tensile load at 0.7 deg * Fis * 1200 lb. What will be the stress at 0 deg * F ? At what temperature will the stress be zero? Assume alpha = 6.5 * 10 ^ - 6 in ./(in*^ F) and E = 29 * 10 ^ 4 psi.
- 3. A cylindrical rod is fixed between two walls. The rod is composed of two materials. Section AC is made of one material (GAC = 2G) while section CD is made of a different material (GcD = G). A torque, T, is applied at point B, as shown below. Jac = JcD = J = 2 in. GẠC = 2G = 20 x 10ʻ psi T= 300 kip in. GCD = G = 10 × 106 psi A D 2L Determine the reactions at the wall, Ta, and Tp. Specify the direction for each. (Note: this is an example of a no calculator problem.) Ans: TA = 250 kip in ( Tp=50 kip in ( T Fixed Fixed to wall to wall(b) shown in Figure 1(b). The tube and the bar are of the same initial length. The combination is compressed between two rigid parallel plates by a force of 500 kN. The diameter of the steel bar is 40 mm, and the inside and outside diameters of the alloy tube are 60 mm and 100 mm respectively. The Young's moduli for steel and aluminium alloy respectively are Est = 200 GNM2, EAI = 70 GNm 2. An assembly of a steel bar enclosed within an aluminium alloy tube is Find the stresses generated in the steel bar and the aluminium alloy tube. 500 KN Rigid plate Aluminium tube Steel bar Rigid plate 500 kN Figure 1(b)At a temperature of 15˚C, a steel bar just fits between two rigid supports. Its length is L = 5 m, height h = 1 m, and width w = 8 cm. The coefficient of linear expansion is 10.8 x 10^–6/˚C and the modulus of elasticity 200 GPa. Find the thermal deformation developed in this wall if the temperature rises to 50˚C. A.1.890 mm B.0.378 mm C.1.620 mm D.3.888 mm Find the stress developed in this wall if the temperature rises to 45˚C. A.75.600 MPa B.18.262 MPa C.7.344 MPa D.94.808 MPa Find the axial force is developed in this wall if the temperature rises to 45˚C. A.5184 kN B.588 kN C.6048 kN D.3932 kN