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. c) Find the maximum deflection of the cantilever beam.
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Problem 1 A cantilever beam of length L is clamped at its left end (x = 0) and is free at its rig...
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) =...
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...
der 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection...
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...
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...
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...
Problem 2 A beam is clamped at left end. A linearly varying distributed load is applied...
Problem 2 A beam is clamped at left end. A linearly varying distributed load is applied in the downward direction on the beam. The maximum magnitude of distributed load at left end is po per unit length. A couple C is applied at the tip. The flexural rigidity of the beam is El (1) Use beam differential equation to calculate deflection and rotation at the tip. (2) Use Castigliano's theorem to calculate deflection and rotation at the tip. Po
A uniform horizontal beam OA, of length a and weight w per unit length, is clamped horizontally at O and freely supporte...
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...
SOLVE USING MATLAB PLEASE THANKS! The governing differential equation for the deflection of a cantilever beam...
SOLVE USING MATLAB PLEASE THANKS!
The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: 2 dx2 where E is elastic modulus, Izz is beam moment of inertia, y 1s beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x-L...
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...
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...
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
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) =...
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...
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...
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...
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...
Problem 2 A beam is clamped at left end. A linearly varying distributed load is applied in the downward direction on the beam. The maximum magnitude of distributed load at left end is po per unit length. A couple C is applied at the tip. The flexural rigidity of the beam is El (1) Use beam differential equation to calculate deflection and rotation at the tip. (2) Use Castigliano's theorem to calculate deflection and rotation at the tip. Po
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...
SOLVE USING MATLAB PLEASE THANKS!
The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: 2 dx2 where E is elastic modulus, Izz is beam moment of inertia, y 1s beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x-L...
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...
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
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