Homework Answers
ANSWER :
Consider a homogteneous horizontal beam of length L. recall that the deflection y(x) of such a beam satisfies the fourth order differential equation
a)
boundary condition
( No deflection slope zero -left )
( No deflection, zero bending moment - right).
b)
since,
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y(0) = 0,4'0) = 0
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y (0) = c = 0
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der 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection...
dat 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection...
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...
5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y...
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 EI d'y - wo where wois a constant load uniformly d.24 distributed along the length of the beam. The general solution of this equation is y(x) = (1 + c2x + c3 x2 + 4x3 + 2001x4 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded...
Problem 1 A cantilever beam of length L is clamped at its left end (x = 0) and is free at its rig...
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....
3. A cantilever beam of length L is embedded at its right end, and a horizontal...
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) =...
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...
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...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of...
(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,...
A fixed-end beam of length L is loaded by triangularly distributed load of maximum intensity qo...
A fixed-end beam of length L is loaded by triangularly distributed load of maximum intensity qo at B. Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. Problem 10.3.10 У Мв В L |A MA RB RA PROB. 10.3-10
ans all parts please 15) (10 Points) Consider a horizontal beam of length L. with uniform...
ans all parts please
15) (10 Points) Consider a horizontal beam of length L. with uniform cross-section and made out of uniform material. It is resting on the x-axis, with one end at the origin. It is acted upon by a vertical force it's own weight in this simple version). The deflection of the beam at any point x,for 0 <=<L.is given by Ely) = w, where E, I, ware constants. E is the Young's modulus of elasticity of the...
Q2. A simply supported beam AB (Figure 2) supports a uniformly distributed load of q =...
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...
th L and carries loading such P.2.5 The cantilever beam shown in Fig. P.2.5 is rigidly...
th L and carries loading such P.2.5 The cantilever beam shown in Fig. P.2.5 is rigidly fixed at Airy stress function relating to the problem is 40bc3 Find the loading boundary conditions. ni mattern corresponding to the function and check its validity with respeet to the stress function satisfies the biharmonic equation. The beam is a cantilever under a uniformly distributed load of intensity w/unit area with a self-equilibrating stress application given by ơ.-n(12c"y-20y3)/40bc3 at x-0. There is zero shear...
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...
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 EI d'y - wo where wois a constant load uniformly d.24 distributed along the length of the beam. The general solution of this equation is y(x) = (1 + c2x + c3 x2 + 4x3 + 2001x4 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded...
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) =...
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...
(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,...
A fixed-end beam of length L is loaded by triangularly distributed load of maximum intensity qo at B. Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. Problem 10.3.10 У Мв В L |A MA RB RA PROB. 10.3-10
ans all parts please
15) (10 Points) Consider a horizontal beam of length L. with uniform cross-section and made out of uniform material. It is resting on the x-axis, with one end at the origin. It is acted upon by a vertical force it's own weight in this simple version). The deflection of the beam at any point x,for 0 <=<L.is given by Ely) = w, where E, I, ware constants. E is the Young's modulus of elasticity of the...
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...
th L and carries loading such P.2.5 The cantilever beam shown in Fig. P.2.5 is rigidly fixed at Airy stress function relating to the problem is 40bc3 Find the loading boundary conditions. ni mattern corresponding to the function and check its validity with respeet to the stress function satisfies the biharmonic equation. The beam is a cantilever under a uniformly distributed load of intensity w/unit area with a self-equilibrating stress application given by ơ.-n(12c"y-20y3)/40bc3 at x-0. There is zero shear...
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