The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 90 GPa] with a cross-sectionalarea of A1 = 510 mm². Bar (2) is an aluminum alloy [E = 68 GPa] with a cross-sectional area of A2 = 320 mm². A concentrated load of P- 75 kN acts on the structure at D. Assume L1-840 mm., L2-420 mm., a-650 mm., b-260 mm., and c-1070 mm. Determine:(a) the normal stresses o1,02 in both bars (1) and (2).(b) the downward deflection vp of point D on the rigid bar.L2BbDAnswers:(a) oi =iMPa, 02 = iMPa(b) VD -imm.

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Answered: The pin-connected structure consists of…

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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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.
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 5.2-m-long aluminum tube (1) is to be connected to a 2.2-m-long bronze pipe (2) at B. When put in place, however, a gap of 9 mm exists between the two members, as shown. Aluminum tube (1) has an elastic modulus of 69 GPa and a cross-sectional area of 1980 mm2. Bronze pipe (2) has an elastic modulus of 93 GPa and a cross-sectional area of 3970 mm2. If bolts are inserted in the flanges and tightened so that the gap at B is closed, determine: (a) the normal stresses ?1, ?2 produced in each of the members. (b) the displacement (change in length of material (2), up is positive) uB of flange B with respect to support A. 5.2 m 2.2 m Answers: (a) 0₁ = (b) Ug = C (1) B (2) -95.40 1.126 9 mm MPa, 0₂ = mm. -47.58 MPa
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
Compound axial member ABC has a uniform diameter of d = 1.25 in. • Segment (1) is an aluminum [E1 = 10000 ksi] alloy. The length of segment (1) is L1 = 100 in. • Segment (2) is a copper [E2 = 17000 ksi] alloy. The length of segment (2) is L2 = 140 in. When axial force Pis applied, a strain gage attached to copper segment (2) measures a normal strain of ɛ2 = 2300 uin./in. in the longitudinal direction. What is the total elongation of member ABC? L2 (1) Aluminum B (2) Copper Answer: in, AL = i
3) The rigid link is supported by steel wire (1) with an unstretched length of 200 mm and cross-sectional area of 22.5 mm?. Member (2) is a short aluminum of initial length 50 mm and cross-sectional area of 40 mm?. The modulus of elasticity of the steel wire is 200 GPa and the aluminum block is 70 GPa. a) Draw the deflected shape of the rigid member and clearly label the deformation of members (1) and (2). b) Write the equilibrium and compatibility equations needed to solve the problem along with the supporting sketches. Hint: Be sure to carefully consider if the members are elongating or shortening; this must be represented mathematically. c) Calculate the internal forces in both axial members and clearly indicate tension or compression. [Ans. to Check: F2 = 535 N]
The axial assembly consists of a solid 1.13-in-diameter aluminum alloy [E = 8300 ksi, v = 0.27,a = 11.1 x 10-6/°F] rod (1) and a solid 1.59-in-diameter bronze [E = 15100 ksi, v = 0.16, a = 8.7x 10-6/°F] rod (2). Assume L1=17 in., L2=27 in. If the supports at A and C are rigid and the assembly is stress free at 14°F, determine: (a) the normal stresses o1,02 in both rods at 176°F (positive if tensile, negative if compressive). (b) the displacernent ug of flange B (positive if to the right, negative to the left). (c) the change in diameter Ad, of the aluminum rod. B (1) (2) L1 L2 Answers: (a) oj = i 23.253 ksi, o2 = i 11.745 ksi (b) ug = -0.017055 in. (c) Adj = in. 0.0020319
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
The aluminum rod AB (Gal = 27 GPa) is bonded to the brass rod BD (Gbr = 39 GPa). The portion CD of 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
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 32-in.-long bronze [E = 13700 ksi] bar with a cross-sectional area of 1.29 in.2. Bar (2) is a 48-in.-long aluminum alloy [E = 10300 ksi] bar with a cross-sectional area of 2.19 in.2. Assume L1=32 in., L2=48 in., a=25 in., b=57 in., and c=15 in. Both bars are unstressed before the load P is applied. If a concentrated load of P = 26 kips is applied to the rigid bar at D, determine:(a) the normal stresses σ1, σ2 in bars (1) and (2).(b) the downward deflection vD of point D on the rigid bar.
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 bj = 80 mm, d1 = dz 240 mm, b2 = 10 mm, d2 = The di- di %3D %3D 120 mm, and a = 60 mm. Deter- (2) (2) (1) mine the maximum bending stresses produced in both the wooden beam and the aluminum b1 plates if a bending moment M = +6,000 N m is applied about the z axis. Assume that E = 12.5 GPa and E2 = 70 GPa. FIGURE 3 %3D

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