trusscalc_2d's Introduction

trusscalc_2D

MATLAB code that solves a plannar (2D) truss using the displacement (stiffness) method.

Solution of a sample truss

A typical plannar truss is solved using the code. This truss is used as the default example in the code.

Truss Geometry

Boundary conditions

Supports

Node 1 is pinned and node 9 is free to move only on the x-axis (x-roller).

Loads

Nodes 3,5 and 7 are subjected to a force of 50 kN with direction in the negative y-axis.

Results

  Node   x displacement [m]   y displacement [m]     x Force [N]     y Force [N]
     1                    0                    0      -7.713e-10         7.5e+04
     2              0.00025            -0.000303               0               0
     3             3.75e-05           -0.0005686               0          -5e+04
     4             0.000175           -0.0007237               0               0
     5             0.000125           -0.0007914               0          -5e+04
     6              7.5e-05           -0.0007237               0               0
     7            0.0002125           -0.0005686               0          -5e+04
     8            5.514e-19            -0.000303               0               0
     9              0.00025                    0               0         7.5e+04

Member   Area [m^2]       E [Pa]       Force [N]          Strain     Stress [Pa]
     1     1.00e-02     2.00e+11      -1.061e+05      -5.303e-05      -1.061e+07
     2     1.00e-02     2.00e+11         7.5e+04        3.75e-05         7.5e+06
     3     1.00e-02     2.00e+11       1.061e+05       5.303e-05       1.061e+07
     4     1.00e-02     2.00e+11        -1.5e+05        -7.5e-05        -1.5e+07
     5     1.00e-02     2.00e+11      -3.536e+04      -1.768e-05      -3.536e+06
     6     1.00e-02     2.00e+11        1.75e+05        8.75e-05        1.75e+07
     7     1.00e-02     2.00e+11       3.536e+04       1.768e-05       3.536e+06
     8     1.00e-02     2.00e+11          -2e+05         -0.0001          -2e+07
     9     1.00e-02     2.00e+11       3.536e+04       1.768e-05       3.536e+06
    10     1.00e-02     2.00e+11        1.75e+05        8.75e-05        1.75e+07
    11     1.00e-02     2.00e+11      -3.536e+04      -1.768e-05      -3.536e+06
    12     1.00e-02     2.00e+11        -1.5e+05        -7.5e-05        -1.5e+07
    13     1.00e-02     2.00e+11       1.061e+05       5.303e-05       1.061e+07
    14     1.00e-02     2.00e+11         7.5e+04        3.75e-05         7.5e+06
    15     1.00e-02     2.00e+11      -1.061e+05      -5.303e-05      -1.061e+07