A simply supported uniform beam (with length L and flexural rigidity El) carries a moment Mo...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of intensity p per unit length as shown Figure 2 below. Assume the deflection shape to be a polynomial in x, and is given by v (x) = a., + as+ a2 x, where ao, a.呙are constants to be determined. (a) State the boundary conditions for the deflection equation. Using the boundary conditions stated in (a) and the Rayleigh-Ritz method, determine (b) the constants a,...
QUESTION 4 (25 marks) A simply supported beam is loaded by an uniform distributed load, wkN/m, over the span of the beam, L, as shown in Figure Q4. (a) Determine the end reactions at point A and B in terms of w and L. (4 marks) (b) At an arbitrary point, x, express the internal mom (c) Show that the deflection curve of the beam under the loading situation is ent, M(x), in x, w, and L. (5 marks) 24EI...
3. A beam is simply supported on both ends where the flexural rigidity EI-1, the distance between the supports is 8 units, and the load per unit length w(z) = 2 sin ( ) + 3. a) State the boundary-value problem associated with the situation. (6 points) b) Solve the BVP. (10 points) 3. A beam is simply supported on both ends where the flexural rigidity EI-1, the distance between the supports is 8 units, and the load per unit...
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter,...
The flexural strength of a simply supported prismatic beam with depth ‘d’, width ‘b’ and span ‘L’ is determined using a four-point bending test. Two equal loads of value ‘P’ are placed at a distance of L/3 and 2L/3 from the support. a. Calculate the reaction forces at the supports. b. Draw the shear and moment diagrams for the beam. c. What is the location of the maximum moment on the beam? What is the value of the maximum moment?...
SS two BMs midspan deflection The simply supported beam shown below has a span length L = 4.1. Two applied bending moments Mo = 4.6 are applied at either support. Determine the midspan deflection of the beam. Assume El is constant. Show your results to two decimal point and no units. (Hibbeler) M M 2 Answer:
The simply supported beam has length L, elasticity modulus E, and cross-section with moment of inertia I. A concentrated force is applied at half point, as illustrated below 1/2 1/2 o The deflection curve for the the first half of the beam is given by: 21 (2) = + (- +) Obtain the equation for the deflection curve y(x) for L/2 < x < L, where: y2(x) = (Ao + A1 x + A2 x2 + A3 x3) When solving...
The equation of the elastic curve (deflection) for a simply supported beam under uniform load is given by y= 1.7 * 10^-5 x^2 (160 - x^2 + x^3), in which, x is the distance from the left support of the beam to any point on the beam, and y is the deflection, both in meters. Find the rate of change of the deflection of the elastic curve at x m = 2
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1, E. Self-weight of the beam is neglected. P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10]...
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1,E. Self-weight of the beam is neglected P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10] (b)...