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Question: What is my mistake?

Question: What is my mistake?

Ramakrishnan 399 Maple
December 06 2015
1

 

Consider a taper steel plate of uniform thickness t := 25mm as shown in the Fig. In addition to its self weight, the plate is subjected to a point load P := 100N at its mid point. Find the global force vector [F] , global stiffness matrix [K] , displacement in each element (1 and 2) , stresses in each element  (1 and 2) and reaction force at the support.Take E := 2*10^5N/mm2; rho := 8.2*10^(-5)kg/m3;

restart

t__1 := 150:

t__3 := 75:

w := 25:

l := 600:

t__2 := (t__1-t__3)/l*((1/2)*l)+t__3 = 225/2

A__1 := t__1*w = 3750``

A__2 := t__2*w = 5625/2``

A__3 := t__3*w = 1875``

Revised areas:

A__1e := (A__1+A__2)*(1/2) = 13125/4``

A__2e := (A__2+A__3)*(1/2) = 9375/4``

  E := 2*10^11:m2; F__1 := R__1:is support reaction N; F__2 := 100:N;``

rho__1 := 82*10^(-6) = 41/500000  N/mm2

rho__2 := 82*10^(-6) = 41/500000 N/mm2

l := 600:``

Number of elements,

n__e := 2:

l__e := 300 = 300````

q__0 := 100:N/m ; l := 1: m; n__e := 4:  elementsl  l__e := l/n__e: m;

We shall consider a two element system as shown in the Fig.
For element 1 Stiffness matrix K is

                                           Vector[row](2, {(1) = 1, (2) = 2})
K__1 := A__1e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1})) = Matrix([[2625000000000000, -2625000000000000], [-2625000000000000, 2625000000000000]])  Vector(2, {(1) = 1, (2) = 2})

For element 2 Stiffness matrix K is

                                         Vector[row](2, {(1) = 2, (2) = 3})
K__2 := A__2e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1})) = Matrix([[1875000000000000, -1875000000000000], [-1875000000000000, 1875000000000000]])  Vector(2, {(1) = 2, (2) = 3})

Global stiffness matrix obtained by adding all the elemental stiffness matrices and given b

           Vector[row](3, {(1) = 0, (2) = 0, (3) = 0})

K__g := Matrix(3, 3, {(1, 1) = K__1[1, 1], (1, 2) = K__1[1, 2], (1, 3) = 0, (2, 1) = K__1[2, 1], (2, 2) = K__1[1, 2]+K__2[1, 1], (2, 3) = K__2[1, 2], (3, 1) = 0, (3, 2) = K__2[2, 1], (3, 3) = K__2[2, 2]}) = Matrix([[K__1[1, 1], K__1[1, 2], 0], [K__1[2, 1], K__1[1, 2]+K__2[1, 1], K__2[1, 2]], [0, K__2[2, 1], K__2[2, 2]]])  Vector(3, {(1) = 0, (2) = 0, (3) = 0})

For element 1 Load matrix F is

  F__1e := (1/2)*`ρ__1`*A__1e*l__e*(Vector(2, {(1) = 1, (2) = 1})) = Vector[column]([[861/25600], [861/25600]]) Vector(2, {(1) = 1, (2) = 2})

``

For element 2 Load matrix F isNULL

F__2e := (1/2)*A__2e*l__e*`ρ__2`*(Vector(2, {(1) = 1, (2) = 1})) = Vector[column]([[123/5120], [123/5120]]) 

``

 

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Ramakrishnan V

rukmini_ramki@hotmail.com
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