Fixed-fixed beam with a point load at any position.

METHOD

What this calculator solves

This is the single-load, constant-EI solution for a prismatic beam fixed against vertical movement and rotation at both ends. Enter the downward load magnitude P, its distance a from the left support, and the right-hand distance is derived as b = L − a.

Input convention: P is a non-negative downward magnitude; a is measured from the left fixed end and must satisfy 0 < a < L; E is entered in GPa and I in cm⁴. The page displays reaction and moment magnitudes. End moments are identified as hogging, while the load-point moment and deflection are reported as positive magnitudes.

The classic central-point case is recovered at a = L/2: both reactions are P/2, both end-moment magnitudes are PL/8, the midspan sagging moment is PL/8, and the load-point deflection is PL³/(192EI). The endpoint limits are mathematically meaningful, but this page deliberately requires an internal load position so that it remains an off-centre fixed-fixed case.

SCOPE

Assumptions and limitations

• Euler-Bernoulli, linear-elastic beam theory with constant E and I.
• Both supports are perfectly fixed; settlement, joint flexibility, and partial fixity are excluded.
• One transverse point load is included; self-weight and other loads must be modelled separately.
• Shear deformation, axial force interaction, second-order effects, material nonlinearity, and vibration are excluded.
• The reported deflection is at the load position. For an eccentric load, it is not labelled as the absolute maximum deflection along the span.
• This is an analysis aid, not a reinforced-concrete, steel, connection, serviceability, or code-compliance check.

REFERENCES

Further reading

The equation pattern is cross-checkable against the specific fixed-both-ends point-load case in StructX: fixed both ends, point load at any point. For the underlying slender-beam assumptions and boundary-condition method, see MIT OpenCourseWare beam theory notes.