T L/2 The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST has uniform flexural rigidity (El) and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening. R L When the structure is subjected to a concentrated horizontal load P at the end T, the magnitude of rotation at the support R, is

T L/2 The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST has uniform flexural rigidity (El) and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening. R L When the structure is subjected to a concentrated horizontal load P at the end T, the magnitude of rotation at the support R, is

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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First question
The planar structurc RST snown in the figure is roller supported at S and pn supported at R. Mombers RS and ST has uniform flexural rigidiry (El) and S is a rigid joint. Consider only bending deformation and neglect cffects of solf woight and ax al stiffening. L 2 R When the structure is subjected to a concentrated horizontal load P at the end I. the magnitude of rotat on at the support R. is
We are given the statically indeterminate structure shown in Figure 2. Apart from the loadings, member AB is also subjected to temperature effects. The cross-sectional depth of member AB is h = 12 in, and the thermal coefficient is aT= 5:10-6 /° F. We are also given that the effect of axial forces on the deformations can be NEGLECTED. 1 kip/ft 5 kip BV VVvvvwwW EI = 8:105 kip-ft2 EI = 106 kip-ft2 20 ft Figure 2 a) Establish a primary structure b) Establish the compatibility equation from which you will obtain the redundant force c) Determine the support reactions of the structure d) Determine the internal loading diagrams of the structure e) Determine the support reactions IF THE STRUCTURE IS ONLY SUBJECTED TO THE TEMPERATURE EFFECTS (and not the loads) AT: = 5 °F ÅT;= -5 °Fi
B) The free ends of two cantilever beams each of length L and flexural rigidity El are joined together with a spring as shown in Fig. (6). The stiffness of the spring is K = Using the method of consistent deformations, determine the force in the spring due to a concentrated load W acting at center of the lower cantilever. www
2
A pin-connected structure is supported as shown in the figure. Bar (1) is made of brass [E = 105 GPa], and bar (2) is made of an aluminum alloy [E = 70 GPa]. Bars (1) and (2) each have cross-sectional areas of 375 mm². Rigid bar ABCD is supported by a pin in a double-shear connection at B. If the allowable shear stress for pin B is 130 MPa, calculate the minimum allowable diameter for the pin at B when P = 107 kN. P A 880 mm D B 720 mm 430 mm (2) (1) 260 mm 400 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.
PROBLEM NO. 1 For the truss shown, determine the safe value of P if the allowable stress in tension is 148 MPa in tension and 99 MPa in compression. The cross-sectional area of vertical and horizontal members is 1 1980 mm² 12 while that of diagonal members is 889 mm² 1.5P 4.99 m 4.99 m 4.99 m B C D E 3.88 m
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 0.75 in.2 and bar (2) has a cross-sectional area of 0.45 in.2. After load P is applied, the strain in bar (1) is found to be 850 μεμε. Assume L1=53 in., L2=79 in., a=34 in., b=33 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.
A truss is subjected to loads as shown. Assumed AE is constant. Use method of consistent deformation. Determine the Axial force developed in member BC?
The triangular solid plate ABC is restrained by rod (1) at A and pin support at B. After applying the force P, the solid plate tilts around pin B and after closing the gap = 1.9 mm, pushes element (2). What is the strain in rod (1) if the internal strain in element (2) is E2 = -1020 pe? [L₁=620 mm, L₂= 680 mm, a = 300 mm, b = 320 mm, gap= 1.9 mm] L AD (2
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 0.81 in.2 and bar (2) has a cross-sectional area of 0.46 in.2. After load P is applied, the strain in bar (1) is found to be 770 με. Assume L1=55 in., L2=78 in., a=31 in., b=31 in., and c=36 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.