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# Engineering Frame Theory

Structures formed of members that are rigidly connected and designed to resist a load are known as frames, while the same members, if connected by pin connections, are known as trusses. Analytically, trusses are considered to be a special case of frame. For frames, it is assumed that there is no interaction between axial, torsional and flexural deformations and that the responses are based on uncoupled extension, torsion and bending theory.

Fixed connections: sometimes referred to as rigid joints, are capable of transferring axial forces as well as moments. It is not possible for any relative rotations between the two connected members without distortion occurring. Fixed connections demand greater attention during design and construction as they are often the source of failures.

Pinned connections: or pined joints are capable of transferring axial forces only. Because there can be relative rotations between the connected members bending moments are not transferrable.

# Assumptions and Limitations

• The cross-section of the frame members are considered small compared to its length (members are long and thin)
• Loads act transverse to the longitudinal axis and pass through the shear centre (any torsion/twist is eliminated).
• Self weight of the frame members have been ignored (this may have to be added).
• The materials that make up the frame are homogenous and isotropic and have a constant Young's modulus in all directions.
• The young's modulus is considered to be constant in both compression and tension.
• The centroidal planes of the frame members(Neutral surface) sre subjected to zero axial stress and does not undergo any change in length.
• The response to strain is one dimensional stress in the direction of bending.
• Deflections are assumed to be very small compared to the overall length of the members that make up the frame.
• The cross-section of members remain planar and perpendicular to the longitudinal axis during bending.
• Any deflection of the Frame follows a circular arc with the radius of curvature considered to remain large compared to the dimension of the cross section.

A selection of frame equations along with relevant engineering calculators can be found Here.

Additional information regarding engineering beam theory can be found Here.