ENGINEERING – TRUCTURAL ENGINEERING — BEAM & FRAME CALCULATOR
Fixed End Moments
A precise tool.
What is the Fixed End Moments & How does it work?
Fixed‑end moments (FEM) are the moments that would develop at the ends of a beam if both ends were prevented from rotating. They are essential for the stiffness method and for assembling the global stiffness matrix of indeterminate structures.
For a point load (P) applied a distance (a) from the left support of a member of total length (L) (with (b = L-a)), the FEM are derived from equilibrium and compatibility conditions. The load creates a couple that is shared between the two fixed ends.
M_{AB} = -frac{P a^{2} b}{L^{2}},quad M_{BA} = frac{P a b^{2}}{L^{2}}
M_{AB} = moment at the left end, M_{BA} = moment at the right end
Parameters
Result
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Frequently Asked Questions
How do I calculate fixed-end moments for a point load?
Use the formula M = Pab/L, where P is the point load, a is the distance from the left support to the load, b is the distance from the load to the right support, and L is the total length of the beam.
What are fixed-end moments used for?
Fixed-end moments are crucial for stiffness method analysis and assembling the global stiffness matrix in indeterminate structures.
Can you explain the concept of compatibility conditions in this context?
Compatibility conditions ensure that the deflection at the point where two beams meet is continuous, which is essential for accurate structural calculations.
How do I apply a distributed load instead of a point load?
For a distributed load, you need to integrate the load over the beam segment and then apply the fixed-end moment formulas accordingly.
What are the units for fixed-end moments?
Fixed-end moments are typically expressed in force-length units, such as Newton-meters (N·m) or kilogram-force meters (kgf·m).
How do I determine the positions a and b for my beam?
Measure the distance from each end of the beam to the point where the load is applied. ‘a’ is from the left support, and ‘b’ is from the right support.
Can this calculator handle multiple loads on a beam?
This specific calculator is designed for a single point load. For multiple loads, you would need to calculate each fixed-end moment individually and then sum them up.
Results are for informational purposes only and do not constitute professional advice.