*Prob. 2.3-9. A “rigid" beam AD is supported by a smooth pin at D and by vertical rods attached to the beam at points A, B, and C. The rods are all strain free when the beam is horizontal (0 = (0). Subsequently, rod (2) is heated until its extensional strain reaches the value e = (a) Determine the value of the (counterclockwise) beam angle 0 that corresponds to the strain e, = 80.0(10¬") . (b) Determine the corresponding extensional strains e and €3. 80.0(10-") im. L1 = L3 = 30 in., L2 = 40 in., a = 20 in., b 60 in. L2 (2) L1 |(1) -"Rigid"| |A В L3 (3) P2.3-9

*Prob. 2.3-9. A “rigid" beam AD is supported by a smooth pin at D and by vertical rods attached to the beam at points A, B, and C. The rods are all strain free when the beam is horizontal (0 = (0). Subsequently, rod (2) is heated until its extensional strain reaches the value e = (a) Determine the value of the (counterclockwise) beam angle 0 that corresponds to the strain e, = 80.0(10¬") . (b) Determine the corresponding extensional strains e and €3. 80.0(10-") im. L1 = L3 = 30 in., L2 = 40 in., a = 20 in., b 60 in. L2 (2) L1 |(1) -"Rigid"| |A В L3 (3) P2.3-9

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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Pin-connected rigid bars AB, BC, and CD are initially held in the positions shown by taut wires (1) and (2). The bar lengths are a = 36 ft and b = 27 ft. Joint Cis given a horizontal displacement of 5.7 in. to the right. (Note that this displacement causes both joints B and C to move to the right and slightly downward.) What is the change in the average normal strain in wire (1) after the displacement? B (1), a (2) Answer: = i (0)
SOLVE
The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 92 GPa] with a cross-sectional area of A₁ = 680 mm². Bar (2) is an aluminum alloy [E = 74 GPa] with a cross-sectional area of A₂ = 350 mm². A concentrated load of P = 56 kN acts on the structure at D. Assume L₁=900 mm., L2=600 mm., a=580 mm., b=310 mm., and c=1160 mm. Determine: (a) the normal stresses 01, 02 in both bars (1) and (2). (b) the downward deflection vp of point D on the rigid bar. b Answers: (a) o₁ = (b) VD= i i L₁ L2 (2) B C MPa, 0₂ = mm. i D MPa
1. For the roof truss shown in Figure 3, determine the force present in ele- ment GH and in each element located to the right of GH. Also, establish whether the elements are in tension or compression. (I suggest you start from node M applying the method of nodes until you get to element GH) -2.4 m--2.4 m-1.2 m-2.4 m--2.4 m--1.2 m- 1.5 kN 1.5 kN 1.5 kN 1.5 kN D VI 1.5 kN 1 kN В 2.5 m E K 1 kN 1m H M F
The brass rod AB is fixed connected at A. When the temperature is T₁-50 °C, there is a 3 mm gap between its end (point B) and the wall C. The cross-sectional area of the rod is 10 cm². Ignore the weight of the bar. The temperature is now increased to T₂-130 °C and the rod AB is pushing against the wall at C. Ebr = 100 GPa, abr = 20 x 10-6/°C Fallow 70 MPa L = 3m A 3 m B/C с 3 mm a. Draw a FBD for when the temperature is increased to T₂ and write down the force balance for this scenario. Call the reactions at FA and FC. Ton =1) und prit brolim volgen Aistis Intelesa si s b. State the compatibility condition and solve for the reactions at A and C.
strain free, before the lantern is hung. When the lantern is hung, it causes a 50-mm sag in the wire. Determine the Prob. 2.3-6. Determine an expression for the extensional strain e(x) at cross section x (0sxsL) of the hanging con- ical frustum in Prob. 2.2-4, and (b) determine an expression for the total elongation, e, of this hanging conical frustum in Prob. 2.2-4. The conical-frustum rod is made of material for which o = Ee, with E= const. Prob. 2.3-7. For small loads, P, the rotation of "rigid" beam AF in Fig. P2.3-7 is controlled by the stretching of rod AB. For larger loads, the beam comes into contact with the top of col- umn DE, and further resistance to rotation is shared by the rod and the column. Assume (and later show that this is a valid as- sumption) that the angle 0 through which beam AF rotates is small enough that points on the beam essentially move verti- cally, even though they actually move on circular paths about the fixed pin at C. (a) A load P is applied at end F…
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4. Part AB of the bar has a solid circular cross section and part BC has a hollow circular cross section. The bar is fixed at both ends and a 150-in-kip axial torque is applied at B. Suppose that you want to decrease the weight of the bar by increasing the inside diameter of part B. The bar is made of material that will safely support a pure shear stress of 10 ksi. Based on this criterion, what is the largest safe value of the inside diameter? 4 in 2 in 150 in-kip A -14 in 7 in
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The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 116 GPa] with a cross-sectional area of A₁ = 550 mm². Bar (2) is an aluminum alloy [E = 71 GPa] with a cross-sectional area of A₂ = 290 mm². A concentrated load of P = 62 kN acts on the structure at D. Assume L₁=800 mm., L2=560 mm., a-590 mm., b=430 mm., and c=1160 mm. Determine: (a) the normal stresses 01, 02 in both bars (1) and (2). (b) the downward deflection vp of point D on the rigid bar. a b Answers: (a) σ₁ = (b) VD = i (1) L₁ L2 (2) A B MPa, 0₂ = mm. D MPa
1. For the roof truss shown in Figure 3, determine the force present in ele- ment GH and in each element located to the right of GH. Also, establish whether the elements are in tension or compression. (I suggest you start from node M applying the method of nodes until you get to element GH) -2.4 m--2.4 m-1.2 m-2.4 m--2.4 m--1.2 m- 1.5 kN 1.5 kN 1.5 kN 1.5 kN D VI 1.5 kN 1 kN В 2.5 m E Ук 1 kN 1m H F Figura 3. Cercha 3. 2.Determine the force in the elements ED, EH, and GH of the reinforcement (see Figure 4), and establish whether the elements are in tension or compres- sion. (Use the method of sections). Figura 4. Cercha 4. 50 kN 40 kN -2 m -2 m- -2 m- 1.5 m -30 kN 1.5 m B 40 kN 1.5 m