Beam Analysis

Perform a complete beam calculation in minutes. With six support types, and three load types you have the possibility to check a very wide range of beams.

General

Length (mm)

Beam Type

Beam Size

Youngs Modulus E (N/mm²)

Supports

ID	Support Type	x (mm)	Spring Constant
S₀			-
S₁			-

Point loads

ID	x (mm)	F_x (kN)	F_z (kN)
F₀

Moment loads

ID	x (mm)	My (kNm)

Distributed loads

ID	x₀ (mm)	x₁ (mm)	q₀ (kN/m)	q₁ (kN/m)	q_perp,0 (kN/m)	q_perp,1 (kN/m)

Overview input

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Supports legend

Parameter name	Symbol	Unit	Info text
Support position	x	mm	Position of the support along the beam's length (x-axis), measured from the start of the beam.
Fixed support	Fixed	-	A support that prevents all translation and rotation. It can provide horizontal (Rx), vertical (Rz), and moment (MRy) reactions.
Hinged support	Hinged	-	A support (also called pinned) that prevents translation (in X and Z directions) but allows free rotation (about the Y-axis). It provides horizontal (Rx) and vertical (Rz) reaction forces.
Roller support	Roller	-	A support that prevents translation perpendicular to its rolling surface (in the Z-direction) but allows translation parallel to the surface and free rotation. It typically provides only a vertical (Rz) reaction force.
Spring support (x-direction)	k_x	kN/m	A translational spring that resists movement in the horizontal (X) direction. The reaction force is proportional to the displacement (Rx = kx * δx).
Spring support (z-direction)	k_z	kN/m	A translational spring that resists movement in the vertical (Z) direction. The reaction force is proportional to the displacement (Rz = kz * δz).
Rotational spring support (about y)	k_Ry	kNm/rad	A rotational spring that resists rotation about the Y-axis. The reaction moment is proportional to the rotation (MRy = kRy * θy).

Loads legend

Parameter name	Symbol	Unit	Info text
Load position	x	mm	Position (x-coordinate) of loads and moments along the beams length, measured from the start of the beam.
Point load (horizontal)	F_x	kN	A concentrated force acting horizontally along the beam's longitudinal x-axis.
Point load (vertical)	F_z	kN	A concentrated force acting vertically on the beam.
Moment load	M_y	kNm	A concentrated moment applied about the beam's y-axis, causing bending in the XZ plane.
Distributed load start/end position	x₀ / x₁	mm	Start (x0) and end (x1) positions of a distributed load along the beam's x-axis.
Distributed load (transverse, start/end)	q₀ / q₁	kN/m	Intensity of the transversely distributed load at its start (q_0) and end (q_1) positions.
Distributed load (axial, start/end)	q_perp,0 / q_perp,1	kN/m	Intensity of the axially distributed load at its start (q_perp,0) and end (q_perp,1) positions.

Results legend

Parameter name	Symbol	Unit	Info text
Support reaction (horizontal)	R_x	kN	The horizontal reaction force given by a support on the beam to maintain equilibrium in the X-direction.
Support reaction (vertical)	R_z	kN	The vertical reaction force given by a support on the beam to maintain equilibrium in the Z-direction.
Support reaction (moment)	M_Ry	kNm	The reaction moment given by a support on the beam to maintain rotational equilibrium about the Y-axis.
Internal axial force	N	kN	The internal force acting along the longitudinal axis (X-axis) of the beam. Tension if positive, compression if negative.
Internal shear force	V	kN	The internal force acting perpendicular to the beam's axis (in the Z-direction), representing the tendency of beam sections to slide relative to each other.
Internal bending moment	M_y	kNm	The internal moment acting about the beam's y-axis, causing the beam to bend.
Maximum shear force	V_max	kN	The maximum absolute value of the internal shear force (Vz) along the beam, crucial for shear strength verification.
Maximum bending moment	M_y,max	kNm	The maximum absolute value of the internal bending moment (My) along the beam, crucial for bending strength verification.
Maximum displacement (deflection)	δ_z,max; w_max	mm	The maximum vertical displacement (deflection in Z-direction) of the beam from its unloaded position, important for serviceability checks.