A circular steel rod AB of diameter d1,length L and modulus of rigidity G is loaded as shown is figure. A rigid bar BC of length b is rigidly fixed to AB at B such that BC is perpendicular to AB and lies in the horizontal plane. Find the deflection of point C due to (i) Bending of AB (ii) Torsion of AB (iii) Combined bending and torsion L P B

A circular steel rod AB of diameter d1,length L and modulus of rigidity G is loaded as shown is figure. A rigid bar BC of length b is rigidly fixed to AB at B such that BC is perpendicular to AB and lies in the horizontal plane. Find the deflection of point C due to (i) Bending of AB (ii) Torsion of AB (iii) Combined bending and torsion L P B

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The rigid bar AB of negligible weight is supported by a pin at O. When the two steel rods are attached to the ends of the bar, there is a gap A = 4 mm between the lower end of the left rod and its pin support at C. %3D Compute the stress in the left rod after its lower end is attached to the support. The cross-sectional areas are 300 mm2 for rod AC and 250 mm? for rod BD. Use E = 200 GPa for steel. A В 0.75 m 1.5 m > 2 m D
The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 519 mm2; link CE is made of steel (E = 200 GPa) and has a cross-sectional area of 633 mm2. For the 36 kN force shown, determine the deflection of B (mm) *deflection should have a negative sign if compression and positive if tension. Also, your final answer should have two decimal places
Rigid bar ABCD is loaded and supported as shown. Steel [E = 27800 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.63 in.2 and bar (2) has a cross-sectional area of 0.39 in.2. After load P is applied, the strain in bar (1) is found to be 720 με. Assume L1=56 in., L2=89 in., a=30 in., b=37 in., and c=33 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection vD of point D on the rigid bar. (c) the load P.
Rigid bar ABCD is loaded and supported as shown. Steel [E = 28500 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.62 in.² and bar (2) has a cross-sectional area of 0.38 in.². After load P is applied, the strain in bar (1) is found to be 670 μe. Assume L₁=68 in., L₂=94 in., a-35 in., b=39 in., and c-22 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection vp of point D on the rigid bar. (c) the load P. (2) (1) L₁ B C a L2 b C D P
1. The solid 160 mm diameter bar made of steel with a tensile yield strength Syı = 270 MPa is fixed at location O and is loaded at point 4 (at the centre of the bar), as shown in the figure. a) Clearly draw and label the equivalent force moment system at the location of elements H and K about the centre of the bar at O b) Determine the stresses at the location of element H and draw them on the element indicating the orientation of the axes. c) Determine the principal stresses at the location of element H. d) Determine the factor of safety using the Tresca (Maximum Shear Stress) theory at the location of element H. 2 m 8 m B 3 m 5 m 3 m FAB =10 kN K 4 m H A ELEMENT LOCATIONS
Rigid bar ABCD is loaded and supported as shown. Steel [E = 30000 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.75 in.² and bar (2) has a cross-sectional area of 0.425 in.². After load P is applied, the strain in bar (1) is found to be 780 μe. Assume L₁-60 in., L₂=90 in., a=40 in., b=40 in., and c=30 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection VD of point D on the rigid bar. (c) the load P. Answers: (a) σ₁ = (b) VD = i (c) P = Mi i L₁ a (1) B L2 b in. C ksi, 0₂ = i kips. с tel D P ksi.
The cross-sectional dimensions of a beam are shown. Assume b-2.5 in., t-tw-0.25 in. and d=4.25 in. (a) If the bending stress at point K is 2560 psi (T), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress o H K Answers: (a) M₂ = (b) σH = bf i i tw at point H (positive if tension, negative if compression). lb-ft. psi.
Rigid bar ABCD is loaded and supported as shown. Steel [E = 28400 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.82 in.² and bar (2) has a cross-sectional area of 0.41 in.². After load P is applied, the strain in bar (1) is found to be 700 μe. Assume L₁=69 in., L₂-89 in., a=34 in., b=33 in., and c-37 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection VD of point D on the rigid bar. (c) the load P. A Answers: (a) 0₁ = (b) VD = (c) P= i i i L₁ a (1) B L2 b ksi, 0₂ = in. kips. (2) C i D P ksi.
The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross sectional area of 500 mm^2. Link CD made of steel (E = 200 GPa) and has a cross sectional area of 600 mm^2. Determine the deflection at D in mm
Rigid bar ABCD is loaded and supported as shown. Steel [E = 29900 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.73 in.² and bar (2) has a cross-sectional area of 0.47 in.². After load P is applied, the strain in bar (1) is found to be 800 με. Assume L₁-52 in., L₂=90 in., a-36 in., b-34 in., and c-23 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection vp of point D on the rigid bar. (c) the load P. (2) (1) L₁ B C a Answers: (a) σ₁ = (b) VD = (c) P = i i L2 b C ksi, 0₂ = i in. kips. D P ksi.
At a temperature of 53°F, a 0.1 in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [a= 12.7 x 10-6/°F] and bar (2) is stainless steel [a= 10.4 x 10-6/°F]. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. Assume L₁ = 40 in., L₂ = 57 in. (1) B A L₁ Answer: Final temperature = i bo L2 °F.
Rigid bar ABCD is loaded and supported as shown. Steel [E = 30000 ksi] bars (1) and (2) are unstressed before the load P is applied. Bar (1) has a cross-sectional area of 0.75 in.2 and bar (2) has a cross-sectional area of 0.425 in.2. After load P is applied, the strain in bar (1) is found to be 780 μs. Assume L₁-60 in., L₂=90 in., a=40 in., b=40 in., and c-30 in. Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection vp of point D on the rigid bar. (c) the load P. A Answers: (a) 0₁ = (b) VD= (c) P = i i i L₁ a L2 in. (2) ksi, 0₂ = i kips. C D P ksi.