A cantilever beam AB of length L and uniform flexural rigidity El is shown in Fig. Q4(a). It is subjected to uniformly distributed load (udl) of intensity w. Obtain expressions for the tip rotation 6; and the tip deflection 8,. Fig. Q4(b) shows the same cantilever as above subjected to a udl of intensity w over the left half only. Using the above results, or otherwise, determine the tip rotation 0g and the tip deflection 8. B A L, EI Fig. Q4(a) L/2 в L, EI A Fig. Q4(b)

A cantilever beam AB of length L and uniform flexural rigidity El is shown in Fig. Q4(a). It is subjected to uniformly distributed load (udl) of intensity w. Obtain expressions for the tip rotation 6; and the tip deflection 8,. Fig. Q4(b) shows the same cantilever as above subjected to a udl of intensity w over the left half only. Using the above results, or otherwise, determine the tip rotation 0g and the tip deflection 8. B A L, EI Fig. Q4(a) L/2 в L, EI A Fig. Q4(b)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter4: Shear Forces And Bending Moments

Section: Chapter Questions

Problem 4.5.5P: Cantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and...

See similar textbooks

Similar questions

Cantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1
.2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively. Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA. (a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress (b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment?
A cantilever beam has a length L =12 ft and a rectangular cross section (b= 16 in., h=24 in.), A linearly varying distributed load with peak intensity qoacts on the beam, (a) Find peak intensity q,if the deflection at joint Bis known to be 0.18 in. Assume that modulus E= 30,000 ksi. (b) Find the location and magnitude of the maximum rotation of the beam. TITT В h PROBLEM 9.3-15
A fixed beam AB, 5 m long, is carrying a point load at its centre. The moment of inertia of the beam is 60 x 106 mm4 and modulus of elasticity for beam material is 2.2 x 105 N/mm2. End moments are taken to be 40 kN-m. The load at the centre is
For the loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, and (c) the slope at the free end. Assume that El is constant for the beam. Let wo = 10 kN/m, L = 6.0 m, E=190 GPa, and I = 130x 106 mm4. Wo Answer: (b) VA = mm (c) 8A = rad
Q7 / A beam AB of span 10m is simply supported at it's ends. It carries point loads of 4KN & 8KN at 4m & 6m from left hand support respectively. It also carries uniformly distributed loads of (W) KN/m for the right end. If left end reaction is 20KN . Find (W ) & right end reaction?
The 10 m long simply supported beam in Fig. Q3 is loaded as shown at a point 6m from left end. e (1) (ii) (iii) RA 10%N 10 kNm": Fig. Q3 Calculate the support reactions R₁ and RB. Macaulay's method is to be used to find slopes and deflections along the beam. Write a general expression for the bending moment to enable the solution. Calculate the vertical deflection at the load application point. The flexural rigidity of the beam, EI, is 100 MNm².
Q3 A pin-connected beam as shown in Fig. Q3 is pin-supported at A and roller-supported at B and D. The beam is subjected to a point load of 5 kN at E and a uniformly distributed loading of 10 kN/m over region AC. The Young's modulus is 200 GPa, the second moment of area of beam AC is 100×100 mm, and the second moment of area of beam CE is 200×100 mm*. (1) Prove that the beam is stable and determinate. (2) Calculate support reactions at A, B and D of the beam.
200 kN/m 140 kN I (m) 5 10 7.5 Figure.2: Encastré beam under variety of loads Your tasks are as follows: 1- Construct free-body diagram (FBD) to show the reaction forces and moments, and the equivalent force of the distributed load, knowing that the upward reaction force on left side is 200 kN and the reaction moment is clockwise with a value of 1300 kN.m. 2- Show FBD for each required section/cut and include the internal forces and moments. 3- Write the distribution functions of the shear force and bending moment for each cut in the heam. 4- By hand construct diagrams for the shear force and bending moment distributions. 5- Determine the magnitudces and positions of maximum shcar force and bending momcnt.
Q2 (a)_A beam of uniform flexural stiffness EI and span L is simply-supported at its ends as shown in Figure Q2(a); it carries a uniformly distributed vertical load of w per unit length, which induces bending in the yz plane only. Then the reactions at the ends are each equal to 0.5 (wL); if z is measured from the end C, the bending moment at a distance z from C is 1 M = - WLz 2 1 Find the maximum deflection, vmax w/unit length † t't t wL 2 WL 2 Figure Q2 (a) |
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that EI is constant for the beam. Let w = 12 kN/m, L = 6.0 m, E = 215 GPa, and I = 105 x 106 mm4.
For the overhang beam shown below, (a) draw the free body diagram of the beam, (b) draw the shear and moment diagrams, (c) find moment of inertia of its cross-section, (d) determine the maximum bending stress. (e) indicate the stress components on an infinitesimal volume element (3D stress element) located at the point. Neglect the weight of the beam. 8 kN/m 2 cm em A C 25 em B 4 m 2 m 2 cm 20 cm