Problem 4For the shown structure, AB is made by A-36 steel (Est = 200GPA, ast = 12 x 10-67 °C) and BC is made by%|73.1GPA, aal = 23 × 10-6/ °C). Both AB and BC are having circular cross sectional area. Thealuminum (Ealgap between C and the rigid wall at D is initially 0.15 mm. For the following situations, find (1) reaction forces atfixed end A and D (2) Plot the axial load diagramP=400 kN applied at B and there is no temperature-0.15 тm600 mm600 mmvi.changevii.P=400 kN applied and temperature in both AB and BC25°Csegments had dropped ATP=400 kN applied, however, the temperature in ABincreased ATst = 25°C and temperature in BCdecreased ATal = 25°Cvii.B.25 mm50 mm

The free-body diagram of the structure is shown below. Consider the equilibrium of forces in the…

Answered: Problem 4 For the shown structure, AB…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The aluminum rod AB (Gal = 27 GPa) is bonded to %3D the brass rod BD (Gpr = 39 GPa). The portion CD of %3D the brass rod is hollow and has an inner diameter of 40 mm. If the allowable shear stresses for the aluminum and brass are 90 MPa and 70 MPa, respectively, and the allowable angle of twist of the free end A is 6 degrees, determine the maximum permissible value of T. 60 mm 2T 36 mm T 250 mm 375 mm 400 mm
A brass (? =5.6 ? 10^6 ???) and aluminum (? = 3.7 ? 10^6 ???) cylinders are bonded together at B, and are attached to fixed supports A and C. Determine (a) The torsion in AB, (b) The torsion in BC, (c) The maximum shearing stress in AB (d) The maximum shearing stress in BC.
H.W 3 Two aluminum alloy plates (2) are attached to the sides of a wooden beam (1) as shown in Figure 3. mensions of the composite cross section are b1 = 80 mm, d¡ = 240 mm, b2 = 10 mm, d2 = b2 The di- |di 120 mm, and a = 60 mm. Deter- (2) (2) %3D mine the maximum bending (1) a stresses produced in both the wooden beam and the aluminum b1 plates if a bending moment FIGURE 3 +6,000 N m is applied M2 %3D about the z axis. Assume that Ej = 12.5 GPa and E2 = 70 GPa.
Problem # 2. At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140 °C, determine (a) the normal stress in the aluminum rod Ans: A -300 mm Aluminum A = 2000 mm² E = 75 GPa α = 23 x 16-6/°C 0.5 mm -250 mm Stainless steel A = 800 mm² B E = 190 GPa a = 17.3 x 10-6/°C
Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area of 1.58 in. and an elastic modulus of 2430 ksi. Bar (2) has a cross-sectional area of 0.714 in and an elastic modulus of 4110 ksi. Assume Ly-18 in., Lz-47in, Q=6,4 kips, P-3.2 kips, and R-128 kips. Determine the horizontal deflection of end Crelative to end A. (1) Answer: uCA in.
A small aluminum alloy [E= 77 GPa] tee shape is used as a simply supported beam as shown. For this beam, a = 160 mm. The cross- sectional dimensions of the tee shape are b= 22 mm, d = 33 mm, and t= 4 mm. After loads are applied to the beam at B, C, and D, a compressive normal strain of 410 uɛ is measured from a strain gage located at c = 10 mm below the topmost edge of the tee stem at section 1-1. What is the applied load P? %3D %3D %3D 3P Strain gage E Answer:
A steel component is subjected to alternate cyclical loading. The steel follows Basquin's law for high cycle fatigue, o, x N = C, (where the stress amplitude is in MPa). Ignore the geometric detail and assume that Marin's modifying factors are all equal to 1. You are given the minimum stress ain = -213 MPa, the maximum stress omax = 213 MPa. The material data are Tensile strength oUTS = 539 MPa, Basquin's constant c, = 875 MPa, Basquin's exponent a = 0.085. a) Calculate the stress ratio R, the stress amplitude o, in MPa and the mean stress am in MPa. The answers are acceptable with a tolerance of 0.01 for R and of 1 MPa the stresses. R: MPa MPа b) Calculate the corresponding life, in 10° cycles, (tolerance of 0.1 106 cycles) N :
The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 102 GPa] with a cross-sectional area of A₁ = 200 mm². Bar (2) is an aluminum alloy [E = 72 GPa] with a cross-sectional area of A₂ = 640 mm². All bars are unstressed before the load P is applied; however, there is a 2-mm clearance in the pin connection at A. Assume L₁ = 1880 mm, a = 1060 mm, b = 620 mm, c = 480 mm, and L₂ = 1270 mm. If a load of P = 71 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar. (1) L₁ b tc B (2) D L2
Problem 1 An axial force of P is applied to the center of the rigid end plate shown below. If the portion of the load carried by the aluminum plates is half the portion of the load carried by the brass core, (a) determine the value of h, (b) the total load if the stress in the brass is 50 MPa. Brass core (E = 105 GPa) Aluminum plates (E = 70 GPa) Rigid end plate 300 mm 60 mim 40 mm
TWO SOLID CYLINDRICAL RODS ARE JOINED AT B AND LOADED AS SHOWN. ROD AB IS MADE OF STEEL (E = 210 GPa) AND ROD BC OF BRASS (E = 108 GPa). DETERMINE (A) THE TOTAL DEFORMATION OF THE COMPOSITE ROD ABC, (B) THE DEFLECTION OF POINT B. 40 KN 400 mm 600 mm A B C 30 mm 50 KN 50 mm
Narrow bars of aluminum are bonded to the two sides of a thick steel plate as shown. Initially, at T₁ = 70°F, all stresses are zero. Knowing that the temperature will be slowly raised to T₂ and then reduced to T₁, determine (a) the highest temperature T₂ that does not result in residual stresses, (b) the temperature T₂ that will result in a residual stress in the aluminum equal to 58 ksi. Assume aa = 12.8 x 10-6/°F for the aluminum and a = 6.5 × 10-6/°F for the steel. Further assume that the aluminum is elastoplastic with E = 10.9 × 106 psi and ay = 58 ksi. (Hint: Neglect the small stresses in the plate.) Fig. P2.121
Question 2) Knowing that a 0.02-in. gap exists when the temperature is 75 °F, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to -11 ksi, (b) the corresponding exact length of the aluminum bar. 0.02 in. -14 in. Bronze A = 2.4 in² E = 15 x 10 psi a = 12 x 10-6/°F -18 in.- Aluminum A = 2.8 in² E = 10.6 x 105 psi a = 12.9 x 10-6/°F

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