Find the deflection curve for the following beam for 2 cases: for the pictured distribution and with a distributed load of q(x)=(q0/L2)x2
Find the deflection curve for the following beam for 2 cases: for the pictured distribution and...
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. A simply supported beam AB (Figure 2) supports a uniformly distributed load of q = 18kN/m and a concentrated load of P = 23kN at the centre. Consider length of the beam, L = 3m, Young's modulus, E = 200GPa and moment of inertial, I = 30 x 10 mm-. Assume the deflection of the beam can be expressed by elastic curve equations of the form: y(x) = Ax4 + Bx3 + Cx2 + Dx + E. 1) Sketch...
For the cantilever beam shown in figure below, we have derived the deflection curve during the lecture as: r(z)-하-둬뿌 부] 48 Consider the magnitude of the distributed load q 1 N/m, length of the beam L 1 m, Young's modulus E-200 GPa and the 2nd moment of area about the bending axis is 1 = 250 cm". What is the reaction bending moment at the left end in N.m? Ya 2
For the beam and loading shown in the figure, integrate the load distribution to determine the equation of the elastic curve for the beam, and the maximum deflection for the beam. Assume that EI is constant for the beam. Assume EI=25000 kN⋅m2, L=2.4 m, and w0=61 kN/m. (a) Use your equation for the elastic curve to determine the deflection at x=1.5 m. Enter a negative value if the deflection is downward, or a positive value if it is upward. (b)...
4) A simply supported beam carries the distributed load shown. Determine the deflection curve by integration starting from the load equation. What are the angular deflections at A and B? jimborcan A B II
4) A simply supported beam carries the distributed load shown. Determine the deflection curve by integration starting from the load equation. What are the angular deflections at A and B? 90 А B
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
The deflection of a uniform beam subject to a linearly increasing distributed load can be computed by using the following equation: y = ( 120EIL Given that L 600 cm, I 30,000 cm, wo-2500 N/cm, and E 50,000 KN/cm2 2. Develop a Matlab code that would implement the Golden-Section search method to find the maximum deflection until the error falls below 1% with initial guesses of Xi = 0 and Xu-L. Display all of the following: xl, xu, d, x1...
31 The beam deflective curve equation for sections 0 <I<L and L<I<L, The beam deflection dc at the mid-point of the beam where I = LL (12) (5) Total Marks: (25) Hints for Question 3 1) The bending moment M(x) for the beam AB may be simplified to two separate expressions for cach of the sections such that M (3) 90 24L L40 (51°c – 12x®L+8x"), for 06135 (-2+L), for ££<3<1 M2(x) 24 QUESTION 3 Consider a simple beam AB...
(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,...