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Frames and Trusses

1 tool in the Structures area.

Truss and Frame Analysis

Plane trusses and rigid frames by the direct stiffness method. The structure is typed as text: nodes with coordinates, members with their end nodes and E, A, I (defaults filled in from the unit inputs), supports by code (pin, roller-x, roller-y, fixed, or restraint flags with optional settlements), joint loads and, for frames, uniform and point loads on the members with their fixed-end forces; member ends may be released (pin_i, pin_j). The tool assembles and solves the global stiffness equations by Gaussian elimination with pivoting, names a mechanism or a missing support when the matrix is singular, and reports joint displacements and rotations, reactions with the equilibrium check, member end forces, axial forces and stresses, the extreme shear and moment of every frame member, a figure of the deformed structure with its supports and loads, moment and shear diagrams drawn on the frame and the internal-force diagrams of a chosen member. The default is the three-bar truss of McGuire, Gallagher and Ziemian (Matrix Structural Analysis, 2nd ed., Examples 3.1 and 3.2), whose printed displacements 0.871 / 1.244 / −0.193 mm, reactions and bar forces 90.0, −63.6 and 516.2 kN the page reproduces; their Example 5.7 frame and a fixed-base portal frame checked against Kleinlogel's closed forms are offered in the example select.

1 worked example reproduced, listed on the tool page.

Other Structures sections

Materials · Composites · Beams · Loads and Dynamics · Joints · Stress and Strain · Stability · Plates and Shells · Thin-Walled Structures · Contact · Stress Concentrations · Fatigue · Damage Tolerance