For convenience, support types are described for beams, but apply to other horizontal elements, like trusses, as well. The type of support affects analysis and design, as well as performance. Given the three equations of statics defined above, ΣH=0, ΣV=0, and ΣM=0, beams with three unknown reactions are considered determinate (as described below) and can be analyzed by the three static equations. Beams with more than three unknown reactions are considered indeterminate and cannot be analyzed by the three static equations alone. A beam with two pin supports (1 has four unknown reactions, one horizontal and one vertical reaction at each support. Under load, in addition to bending, this beam would deform like a suspended cable in tension, making the analysis more complex and not possible with static equations.
By contrast, a beam with one pin and one roller support (2) has only three unknown reactions, one horizontal and two vertical. In bridge structures such supports are quite common. To simplify analysis, in building structures this type of support may be assumed, since supporting walls or columns usually are flexible enough to simulate the same behavior as one pin and one roller support. The diagrams at left show for each support on top the physical conditions and below the symbolic abstraction.
1 Beam with fixed supports at both ends subject to bending and tension
2 Simple beam with one pin and one roller support subject to bending only
3 Beam with flexible supports, behaves like a simple beam
Simple beams, supported by one pin and one roller, are very common and easy to analyze. Designations of roller- and pin supports are used to describe the structural behavior assumed for analysis, but do not always reflect the actual physical support. For example, a pin support is not an actual pin but a support that resists horizontal and vertical movement but allows rotation. Roller supports may consist of Teflon or similar material of low friction that allows horizontal movement like a roller.
![]()
By contrast, a beam with one pin and one roller support (2) has only three unknown reactions, one horizontal and two vertical. In bridge structures such supports are quite common. To simplify analysis, in building structures this type of support may be assumed, since supporting walls or columns usually are flexible enough to simulate the same behavior as one pin and one roller support. The diagrams at left show for each support on top the physical conditions and below the symbolic abstraction.
1 Beam with fixed supports at both ends subject to bending and tension
2 Simple beam with one pin and one roller support subject to bending only
3 Beam with flexible supports, behaves like a simple beam
Simple beams, supported by one pin and one roller, are very common and easy to analyze. Designations of roller- and pin supports are used to describe the structural behavior assumed for analysis, but do not always reflect the actual physical support. For example, a pin support is not an actual pin but a support that resists horizontal and vertical movement but allows rotation. Roller supports may consist of Teflon or similar material of low friction that allows horizontal movement like a roller.
