Computer Modelling: Connections, Interpretation, and Limitations

Modelling Connections

• End releases can model force-displacement constraints at connections.

  • A moment release allows relative rotation between the element and the adjacent note, transferring no moment.

  • An axial release allows relative movement along the axis of the member.

  • A shear release allows relative movement perpendicular to the axis of the member.

Structural Actions

• Computer modelling can account for temperature effects, using a material property called the coefficient of thermal expansion, which has units of strain per degree of temperature, and measures the amount of strain induced by a unit temperature change.

  • By a happy coincidence, steel and concrete have approximately the same coefficient of thermal expansion, about 6.5x10^-6/°F

Statically Determinate vs. Indeterminate Structures

• Statically determinate: A structure where there is a unique set of reactions and distribution of internal forces which satisfy equilibrium.

• Statically indeterminate: A structure where there is are multiple sets of reactions and distributions of internal forces which satisfy equilibrium.

• Since a determinate structure has only one pattern of reactions and internal forces that keeps it in equilibrium, that pattern does not change if member sizes are changed or if there are temperature changes or support movements.

• In contrast, since an indeterminate structure has multiple patterns of reactions and internal forces that satisfy equilibrium, the pattern will change when member sizes are changed or with temperature changes or support movements.

  • When members in an indeterminate structure deflect together, the members tend to resist load in proportion to their stiffness.

    • e.g., the stiffer elements do more work.

    • This is called the principle of relative stiffness.

Limits of Linear Analysis

• RISA and most computer programs widely used in practice are based on linear elastic theory. This theory assumes the following:

  • The difference between the deformed and undeformed geometry is negligible.

  • Members and connections have symmetric behavior in tension and compression.

  • Materials do not yield, remaining in the linear range at all stress levels.

• These assumptions are reasonable for many conventional structures under service loads, but there are many important situations which cannot be modelled well using this theory.

  • Cable structures.

  • Post yield behavior.

  • Post-buckling behavior.

  • Global stability problems.