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 forthe 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 theleft half only. Using the above results, or otherwise, determine the tip rotation 0g and thetip deflection 8.BAL, EIFig. Q4(a)L/2вL, EIAFig. Q4(b)

For the uniformly distributed load on the whole span; Let the origin be at the fixed end, At a…

Answered: A cantilever beam AB of length L and…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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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 simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg - 35kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. A Ay- 58.66 - Dy- Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x Dy
Given the beam shown below (E=200GPa, I=180x106 mm4, 80mmx300mm), do the following: a. Draw the shear force and bending moment diagrams b. Find the magnitude and location of the maximum tensile bending stress c. Using superposition, find the elastic curve and then the deflection of the beam at B, C, and D 8kN 4kN A B 4m 3m 3m
Q2(a) A simple beam is shown in Figure Q2(a) has three concentrated loads at the position indicated. The beam cross section is circular with diameter 200mm, determine, (i) support reactions; (ii) maximum bending moment; (ii) maximum bending stress. 100 kN 150 kN 100 kN A B D 2.8 m 2.8m 3 m 2.2m Support-1 Support-2 Figure Q2(a) E.
For the beam and loading shown, use discontinuity functions to compute(a) the slope of the beam at C (positive if counterclockwise and negative if clockwise).(b) the deflection of the beam at C.Assume LAB = 210 mm, LBC = 140 mm, LCD = 120 mm, LDE = 260 mm, MB = 200 N-m, P = 1080 N and a constant value of EI = 590 × 106 N-mm2 for the beam.
A propped cantilever steel beam is constructedfrom a W12 x 35 section. The beam isloaded by its self-weight with intensity q. The lengthof the beam is 11.5 ft. Let E = 30,000 ksi.(a) Calculate the reactions at joints A and B.(b) Find the location of zero moment within span AB.(c) Calculate the maximum deflection of the beamand the rotation at joint B.
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.
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
. The cantilever beam shown below has a length L, moment of inertia I, and is made from a material with modulus of elasticity E. The load P is applied at the end of the beam. a. Derive the maximum deflection of the beam and show that max Ely" (x) P PL³ ЗЕІ' b. Consider E = 29 x 10³ ksi, P = 6 kip, I = 204 in 4, and L = 15 ft with the length and moment of inertia measured with ±5% and ±10% accuracy, respectively. In 3 significant figures, calculate the deflection and express the variation of its worst-case error. 8max Hint: M(y) =
h F The beam of length 5.9 (m) and cross section base 0.10 (m) and height 0.16 (m) shown is made of plain steel with a modulus of elasticity of 200 (Gpa) and an ultimate strength of 400 (Mpa). The load is 250 (N) and the point q is 4.0 (m) from the wall in the x direction. What is the magnitude of vertical deflection of the beam at point q in units of meters?
50 N/m. 3. For the beam shown below, let wo = 90 N/m and w = Wo W1 | A -2 m 2 m 3 m 3 m -2 m Figure 2 Loaded Cantilever Beam a. Find the reactions at A. b. Find the loading function q(x) using singularity functions. c. Find the shear and moment functions V(x) and M(x). d. Determine and plot the shear diagram for the given loading conditions. e. Determine and plot the moment diagram.
The beam AB shown in the figure supportsa uniform load of intensity 3000 N/m acting over halfthe length of the beam. The beam rests on a foundationthat produces a uniformly distributed load overthe entire length.(a) Draw the shear-force and bending-momentdiagrams for this beam.(b) Repeat part (a) for the distributed load variationshown in Fig. b.

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