5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y...
der 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y (x)of such a beam satisfies the fourth order differential equation ELY wo where Wo is a constant load uniformly distributed along the length of the beam. The general solution of this equation is y () = C1 +223 + c3x2 + 423 + 2457 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded on the right...
dat 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y(x)of such a beam satisfies the fourth order differential equation Erd'y w where wois a constant load uniformly distributed along the length of the beam. The general solution of this equation is y(x) = c + C2# + 03 72 +423 + (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded on the right (b) Solve the...
Problem 1 A cantilever beam of length L is clamped at its left end (x = 0) and is free at its right end (x = L). Along with the fourth-order differential equation EIy(4) = w(x), it satisfies the given boundary conditions y(0) = y′(0) = 0,y′′(L) = y′′′(L) = 0. a) If the load w(x) = w0 a constant, is distributed uniformly, determine the deflection y(x). b) Graph the deflection curve when w0 = 24EI and L = 1....
Question. 4 (20%) A uniformly loaded beam of length "L" is supported at both ends. The deflection y(x) is a function of horizontal position x and is given by the differential equation on dEl d1 Beat dE 4() Assume q(x) is constant. Determine the equation for y(x) in terms of different variables. Hint: Use laplace transform. Below are boundary conditions: (L)ono dene y"(o) o no deflection at x= 0 and L no bending moment at x 0 and L y...
Solve equation (4) in Section 5.2 FIdywx) dxA (4) subject to the appropriate boundary conditions. The beam is of length L, and wo is a constant. (a) The beam is embedded at its left end and simply supported at its right end, and w(x) wo, 0 < x < L. усх) (b) Use a graphing utility to graph the deflection curve when wo 48EI and L = 1. = y y 0.2 0.4 0.6 0.8 1,0 0.2 0.4 0.6 0.8...
3. A cantilever beam of length L is embedded at its right end, and a horizontal compressive force of P pounds is applied at the free left end of the beam. When the origin is taken as its free end, the deflection of the beam can be shown to satisfy the differential equation Ely" = -Py – w(x)} Find the deflection of the cantilever beam if w(x) = Wox, 0 < x < L, and y(0) = 0, y'(L) =...
Problem statement Beam Deflection: Given the elastic deflection equation for a beam with the boundary and loading conditions shown below, determine the maximum downward deflection (i.e. where dy/dx = 0) of a beam under the linearly increasing load wo = 10 kN/m. Use the following parameter values: L = 10m, E = 5x108 kN/m², 1 = 3x10-4 m4. Use the initial bracket guesses of XL = 0 m and xu = 10 m. Wo. wol(x5 + 2L?x3 – L^x), (1)...
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...
A uniform horizontal beam OA, of length a and
weight w per unit length, is clamped horizontally
at O and freely supported at A. The transverse
displacement y of the beam is governed by the
differential equation
where x is the distance along the beam measured
from O, R is the reaction at A, and E and I are
physical constants. At O the boundary conditions
are y(0) = 0 and . Solve the
differential equation. What is the boundary...
(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,...