Equivalent Nodal Load Calculator
Convert distributed or point loading on a two-node Euler–Bernoulli beam element into the consistent local nodal load vector, then verify total force and moment equilibrium.
Equivalent Nodal Load Calculator inputs
Define one two-node beam element, its load shape and local sign convention. The four reported terms are the two nodal shears and two consistent end moments.
Equivalent Nodal Load Calculator results
How to use the equivalent nodal load calculator
The equivalent nodal load calculator integrates cubic Hermite beam shape functions against uniform, linearly varying or concentrated transverse loading. Independent equilibrium checks compare the vector with the original force and moment.
Consistent versus lumped nodal loading
This equivalent nodal load calculator integrates the cubic Hermite beam shape functions against the applied transverse load. The result is the consistent four-component local vector consisting of node-1 shear, node-1 bending moment, node-2 shear and node-2 bending moment. A simple half-and-half force split is not generally equivalent because it omits the work-conjugate rotational terms.
Uniform and linearly varying loads
For a uniform load, the two nodal forces are equal and the end moments have equal magnitude with opposite signs. For a linearly varying load, the calculator uses the exact shape-function integrals rather than replacing the trapezoid with a single resultant. This preserves the finite-element virtual-work relationship for the selected beam interpolation.
Point load inside an element
A point load is distributed to the four local degrees of freedom by evaluating the beam shape functions at the entered position. Moving the load toward either node changes both shears and both moments continuously. The position must fall within the element length.
Local axes and engineering use
The displayed vector is local to one planar Euler–Bernoulli element and uses the chosen sign convention. A structural program may order degrees of freedom differently or transform the vector to global axes. Confirm element orientation, releases, shear-deformation assumptions and software conventions before inserting the values into an analysis model.
Equivalent Nodal Load Calculator questions
Why are moments included in an equivalent nodal load?
Beam rotational degrees of freedom are work-conjugate to nodal moments. Consistent loading therefore includes end moments as well as transverse forces.
Does the calculator give support reactions?
No. It produces an element load vector. Support reactions require assembly of the structural model, boundary conditions and solution of the global equations.
Can I use the result for a Timoshenko beam?
The formulas shown are for standard Euler–Bernoulli cubic interpolation. A Timoshenko or specialized element can use different interpolation and loading expressions.