IV. An Aluminum bar AD (see figure) has a c loaded by forces P1 = 7560 N, P2 = 5340 segments of the bar are a = 1525 mm, b (a) Assuming that the modulus of elasticity i length of the bar. Does the bar elongate or s (b) By what amount P should the load P3 be change in length when the three loads are a (c) If P3 remains at 5780 N, what revised cr result in no change of length when all three A B₁ P₁
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- (40 How A Rismatic steel bar of a Square cro ss section (looxlo0)mm is loaoled by Compressive force P= 1300 K, the bar has length 2.5 m, Eg=200GPay V=0.3,determine the shortening 8, the increase in the dimensions of cross Section, the change in Volume DV of the bar? loomm loommPROBLEM 01: Hollow bar length is 1.40m long and tube length is three-fourth as long as the bar. Torque T=1100N.m acts at the free end of the bar. Both the bar and tube are made of an aluminum alloy with shear modulus of w ww elasticity G=27GN/m². Given that dl=35mm, d2=45mm, d3=60mm, d4=70mm. Determine the following: a. Maximum shear stress in both the bar and tube b. Angle of twist at the end A of the bar. (In degrees) Tube Fixed plate End plate Tube d3 d1 d2 d4 Bar Cross-section of the bar and tubeDuring laboratory testing of an 8-inch aluminum-alloy rod with a cross sectional area of 0.32in, a tensile load of 40,000 lbs.is applied. If the cross sectional area decreases to 0.3188in and lengthens to 8.021 inches, what is the Modulus of Elasticity and Poisson's Ratio? 29. E= 6/8 v =-ɛ(lateral)/E(axial)
- a. A round steel bar with an initial diameter of 20 mm and length of 2 m is placed in tension, supporting a load of 2000 kg. If the Young's modulus of the bar is 200 GPa what is the length of the bar when supporting the load (assuming it does not yield)? b. If the Poisson's ratio of the steel is 0.4, what will the diameter of the bar be when supporting the load?A wood beam is strengthened using two steel plates as shown in the figure below. *Inserted Photo* The beam has simple supports and an overhang and is subjected to a point load and a uniform load as shown in the figure below. Calculate the maximum tensile and compressive stresses of the beam. Assume that Ew = 11 GPa and Es = 200 GPa. (Enter your answers in MPa. Use the deformation sign convention.) maximum tensile stress in wood ? MPa maximum tensile stress in steel ? MPa maximum compressive stress in wood ? MPa maximum compressive stress in steel ? MPaPROBLEM O1: A loadP compresses the bronze core, brass, and steel shell as shown in the figure, which have a length L=5.0". Knowing that moduli of elasticity of the bronze, brass and steel are EBR=14.5x106 psi, EB=15x106 psi and Es=30x106 psi, respectively. The diameters are D1=0.24", D2=0.27", D3=0.34", D4=0.37", and Ds=0.40". Determine the load P that will shorten the assembly by 0.004 in. P -STEEL SHELL BRASS TI || BRONZE CORE || || || || || D D D || || || Ds
- Question Three Three bars each made of different materials are connected together and welded to the two walls when the temperature is T,= supports when the temperature becomes T,= 12°C. The material properties and cross- sectional area of each bar are given in the figure. ... 18°C. Determine the force exerted on the (rigid) %3D %3D Steel Brass Сopper Est = 200 GPa as = 12(10-")/°C abr = 21(10¬)/°C acu Ebr 110 GPa Ecu 130 GPa 17(10 )/°C %3D Acu 515 mm2 450 mm2 %3D Ast 200 mm2 Apbr 300 mm- 200 mm 100 mmA round bar made of same material consists of 3 parts each of 100 mm, length having diameters of 40 mm, 50 mm and 60 mm respectively. If the bar is subjected to an axial load of 10 kN, the total elongation of the bar would be (E is the modulus of elasticity in KN/mm². (a) 4/1 1 1 + + (b) TE 16 25 36 (c) 1 0.4 1 1 + wwwwww + TE 16 25 36 (d) 4√2/1 1 1 www + wwwwwww + TE 16 25 36 40/1 1 1 + TE 16 25 36 — ===== + — mm mm mm mmProperties: Rod 1 8F D = 40 mm d = 20 mm L = 1.3 meter E = 80 Gpa ROD 1 ROD 2 Rod 2 D = 80 mm d = 20 mm L = 1.0 meters E = 80 Gpa 3F 2. The composite rod shown in the figure is composed of three rods rigidly welded together. Applied forces in terms of "F" are exerted in different parts of the composite rod. Compute the maximum safest value of "F" if the allowable total deformation of the composite rod is limited to 0.50 mm only. ROD 3 2F Rod 3 D = 60 mm d = 20 mm L = 1.2 meters E = 80 GPa 7F
- 2.3-7 A steel bar 2.4 m long has a circular cross section of diameter d, = 20 mm over one-half of its length and diam- eter d, = 12 mm over the other half (sce figure part a). The modulus of elasticity is E = 205 GPa. (a) How much will the bar elongate under a tensile load P = 22 kN? (b) If the same volume of material is made into a bar of constant diameter d and length 2.4 m, what will be the clongation under the same load P? (c) If the uniform axial centroidal load q = 18.33 kN/m is applied to the left over segment 1 (sce figure part b), find the ratio of the total elongation of the bar to that in parts (a) and (b). Įd1 = 20 mm Įd2 = 12 mm %3D P= 22 kN 1.2 m- -1.2 m (a) q = 18.33 kN/m [d1 = 20 mm |d2 = 12 mm P = 22 kN 1.2 m (b)Answer all.a.A mild steel flat of width b= 150 mm, thickness t = 20 mm and length L= 6000 mm carries an axial pull P = 300 kN. If modulus of elasticity of mild steel is 200 GPa and Poisson’s ratio is 0.25, calculate the change in length, width and thickness of the flat. B.A stepped bar made of brass is subjected to axial loads as shown in the below figure. Determine the total change in length of the bar. Take E =100 GPa.figure is attached C.A thin cylinder of external diameter 820 mm, length 3 m and wall thickness of 10 mm is subjected to an internal pressure of 2.5 N/mm2 . Determine the change in diameter and length. Take Young’s modulus = 2×105 N/mm2 and Poisson’s ratio = 0.25.A cylindrical bar of steel 9.9 mm (0.3898 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Determine the force that will produce an elastic reduction of 3.0×10-3 mm (1.181 ×10-4 in.) in the diameter. For steel, values for the elastic modulus (E) and Poisson's ratio (v) are, respectively, 207 GPa and 0.30. i N