16-3. Determine the structure stiffness matrix K for eachmember of the frame. Take E = 200 GPa, I = 270(10°) mm,A = 9(10³) mm² for each member.(33 m8 kN/m38.9.-114)-2 m-Prob. 16-3

It is a matrix approach for determining component forces and displacements in structures that make…

Answered: 16-3. Determine the structure stiffness…

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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2.54 The rigid bar AB of negligible weight is supported by a pin at 0. When the two steel rods are attached to the ends of the bar, there is a gap A between the lower end of the left rod and its pin support at C. After attachment, the strain in the left rod is 1.5 x 10-3. What is the length of the gap A? The cross-sectional areas are 300 mm? for rod AC and 250 mm² for rod BD. Use E = 200 GPa for steel. A B 0.75 m -1.5 m 2 m FIG. P2.53, P2.54
Two members AB and AC are made of material with E= 91 Gpa and each member has cross sectional area of A= 290 mm2. The members are used to support bar BC. If P-2079 N, L1= 202 mm , L2= 313 mm and L3= 480 mm. Answer the following questions. L3 E В to L1 L2 The tension in member AB%3D he tension in member The elongation in member AB=
3 The rigid bar EFG is supported by the truss system shown. Determine the cross- sectional area of member AE for which the normal stress in the member is 105 MPa. 0.90 SONRAWING D B R 15 kN -1.2 m 1.2 m-1.2 m-
Q₁: Analyze the truss shown below B с <50k 3m IMI A E 100ku EA is Constant for all members + Am X Am
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
The rigid beam is supported by a pin support at A and steel wires BD and CE (E-200GPA). The steel wires are 1cm in diameter. If the load P is 5kN and the weight of the beam is neglected, solve the deformation at wire BD. E 4 m +2m+2m -3 m O 0.417mm O 0.497mm O 0.329mm O 0.231mm
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 = 520 mm². Bar (2) is an aluminum alloy [E = 77 GPa] with a cross-sectional area of A₂ = 380 mm². A concentrated load of P = 58 kN acts on the structure at D. Assume L₁=730 mm., L₂=440 mm., a=680 mm., b=420 mm., and c=1030 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) 6₁ = (b) VD= i L₁ L2 (2) B с MPa, 0₂ = mm. D P MPa
F ., É, are applied to the truss system. В a) Find member forces in each member and state if the members are in tension or 4 m compression. b) If the maximum force that any member can support is Tmax in tension and Cmax in compression, determine the maximum value of P that can be supported. A E 3 т 3 m 3 т 3 m F1 F2 F3 F4 F5 Tmax Cmax P 2P 40° 7 kN 8 kN 2P Note: Do not show zero forces in your calculations.
3 Determine the support reactions o- the beam shown here: 9 = 150 น max A + 12 hint: 1 resultant force is the area the Loading. 2 the point of action of resultant is not at the middle. ft. 10/ft B + under У
The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 109 GPa] with a cross-sectional area of A₁ = 530 mm². Bar (2) is an aluminum alloy [E = 64 GPa] with a cross-sectional area of A2 = 330 mm². A concentrated load of P = 67 kN acts on the structure at D. Assume L₁=740 mm., L₂=500 mm., a=660 mm., b=310 mm., and c=1030 mm. Determine: (a) the normal stresses 0₁, 02 in both bars (1) and (2). (b) the downward deflection VD of point D on the rigid bar.
2.69 The bars AB, AC, and AD are pinned together as shown in the figure. Hori- zontal movement of the pin at A is prevented by the rigid horizontal strut AE. Cal- culate the axial force in the strut caused by the 10-kip load. For each steel bar, A = 0.3 in.? and E = 29 × 106 psi. For the aluminum bar, A = 0.6 in.² and E = 10 × 106 psi.
The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 110 GPa] with a cross-sectional area of A₁ = 630 mm². Bar (2) is an aluminum alloy [E = 79 GPa] with a cross-sectional area of A₂ = 340 mm². A concentrated load of P = 52 kN acts on the structure at D. Assume L₁=910 mm., L₂=430 mm., a=450 mm., b=280 mm., and c=1030 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 5 Answers: (a) 6₁ (b) VD= = tel i (1) L₁ L2 B C MPa, 0₂ = mm. i MPa

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16-3. Determine the structure stiffness matrix K for each member of the frame. Take E= 200 GPa, I=270(10°) mm“, A = 9(10') mm² for each member. (2 3 (3 3 m 8 kN/m 1. 3 10 8. 9. 11 4 2 m Prob. 16-3 2]