The differential equation satisfied by a beam uniformly loaded ( W kg/ meter ) with one end fixed and the second end subjected to a tensile force-P is given by
El d^2 y/dx^2 = Py - 1/2 Wx^2
Where E is the modulus of elasticity and l is the moment of inertia show that the elastic curve for the beam with condition y = 0 and dy/dx = 0 at x = 0 is given by
y = W/Pn^2 (1-cosh nx ) + Wx^2 /2P where n^2 = ( P/EI)
1
Expert's answer
2020-03-11T14:16:31-0400
Transform the original equation to get less confused with constants
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Dennis Addo
10.05.21, 00:52
2. A light horizontal strut AB is freely pinned at A and B. It is
under the action of equal and opposite compressive force P at its ends
and it carries a load W at its centre. Then for 0 < x < 1 2 , EI d2y
dx2 + P y + 1 2 W x = 0, given y = 0 at x = 0 and dy dx = 0. Use the
Laplace transforms for solving differential equations to show that y =
W 2p ( sin ax a cos at 2 2 x), where a2 = p EI
Assignment Expert
30.11.20, 20:30
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fanni
28.11.20, 11:05
solve the initial value problem x_dx^dy-2y=〖2x〗^4, y(2)=8
Comments
Dear Dennis Addo, please use the panel for submitting a new question.
2. A light horizontal strut AB is freely pinned at A and B. It is under the action of equal and opposite compressive force P at its ends and it carries a load W at its centre. Then for 0 < x < 1 2 , EI d2y dx2 + P y + 1 2 W x = 0, given y = 0 at x = 0 and dy dx = 0. Use the Laplace transforms for solving differential equations to show that y = W 2p ( sin ax a cos at 2 2 x), where a2 = p EI
Dear fanni, please use the panel for submitting new questions.
solve the initial value problem x_dx^dy-2y=〖2x〗^4, y(2)=8