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Maple Session 3:

Truss Analysis

Learning Objectives:

-  Truss analysis using Maple

Maple Commands Used

-  genmatrix

-  submatrix


Truss Analysis

> / restart:
> / with(linalg):

Manipulating Matrices

Warning, the protected names norm and trace have been redefined and unprotected

> / m1:=matrix(3,3, [1,2,3, 4,5,6, 7,8,9]);

Sub-Matrix

In some cases, the user only wishes to use part of the matrix. In this case the submatrix command can be used to extract a portion of the matrix. The command has 3 parts to its syntax: the matrix to be partitioned, the inclusive range of rows being used, and the inclusive range of columns being used.

> / m2:=submatrix(m1, 1..2, 2..3);

Generating a Matrix

In other cases, the user will have a set of equations that need to be put in matrix form. Previously, this was done manually. However, the genmatrix command will do this for us automatically.

> / eq1:=2*x+y*3=0;
> / eq2:=y-6*x=5;

The command has 3 parts to its syntax: a list of equations to be combined, the variables in the equations, and the optional "flag." If "flag" is used, then the augmented matrix is created. If "flag" is not used, the only coefficient matrix is formed.

> / A1:= genmatrix({eq1,eq2}, [x,y]);
> / A2:= genmatrix({eq1,eq2}, [x,y], flag);


Sample Problem

> / restart; with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected
a) Determine the reaction forces at A and C.

b) Determine the internal forces on the members.

Sum the forces acting on pin A

> / eqAx:=0=Ax+Fab+(3/5)*Fad;
> / eqAy:=0=Ay+(4/5)*Fad;

Sum the forces acting on pin B

> / eqBx:=0=-Fab+Fbc;
> / eqBy:=0=Fbd;

Sum the forces acting on pin C

> / eqCx:=0=-Fbc-(3/5)*Fcd; eqCy:=0=Cy+(4/5)*Fcd;

Sum the forces acting on pin D

> / eqDx:=0=-(3/5)*Fad+(3/5)*Fcd+100; eqDy:=0=-(4/5)*Fad-Fbd-(4/5)*Fcd-200;

Create the augmented matrix

> / AugMat:=genmatrix({eqAx,eqAy,eqBx,eqBy,eqCx,eqCy,eqDx,eqDy}, [Ax,Ay,Cy,Fab,Fad,Fbc,Fbd,Fcd], flag);

Place the matrix in reduced row echelon form

> / RrefMat:=evalf(rref(AugMat));

Part A

Listing forces Ax, Ay, and Cy

> / solnA:=submatrix(RrefMat, 1..3, 9..9);

Part B

Listing forces Fab, Fad, Fbc, Fbd, and Fcd

> / solnB:=submatrix(RrefMat, 4..8, 9..9);


Maple 3

Directions: Complete the following problems using Maple

Michael Guerci

2004-10-26

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  1. The plane truss forms part of the support of a crane on an offshore oil platform. The crane exerts vertical 80-kN forces on the truss at B, C, and D. You can model the support at A as a pin support and model the support at E as a roller support that can exert a force normal to the dashed line but cannot exert a force parallel to it. The angle a = 30°.
  2. Determine the reaction forces at A and E
  3. Determine the internal forces on the members

Michael Guerci

2004-10-26