F = 10,000 lb A = 2 in2 E = 30 x 106 psi L = 10 ft θ = 45° Finite Element Method (FEM) Finite Element Analysis (FEA) Computer Aided Engineering (CAE) 2 F = 10,000 lb A = 2 in2 E = 30 x 106 psi L = 10 ft θ = 45° 3 L θ 1 4 F L

Element 1 l and m are direction cosines E Modulus of Elasticity A Cross Sectional Area L Length of the Truss Element

Element 1 1x 1y 2x 2y 2 1x 1y L 2x 2y 1 F

Element 1 1x 1y 2x 2y 2 1x 1y L 2x 2y 1 F

Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

Element 2 1x 1y 3x 3y 1x 3 1y 3x 3y θ 1 F

Element 3 1x 1y 4x 4y 1x 4 1 1y F 4x L 4y

Element 3 1x 1y 4x 4y 1x 4 1 1y F 4x L 4y

Total Stiffness Matrix 1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

Total Stiffness Matrix 1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

Total Stiffness Matrix 1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

Total Stiffness Matrix 1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

Force and Displacement Vectors

Expand the matrix and reorganize the information {F}=[K]{d} Expand the matrix and reorganize the information

{F}=[K]{d} Create A matrix Create B matrix Recall that AX=B X=A-1B Find the inverse using Microsoft Excel Calculate X X= {D1x , D1y , F2x , F2y , F3x , F3y , F4x , F4y}

Solution X = {D1x , D1y , F2x , F2y , F3x , F3y , F4x , F4y}

Displacement and Stress Results

Mechanical Simulation

Mechanical Simulation Results