Beam Properties

Upcoming release

Beam elements will be available with the upcoming release

Syntax

*Beam properties
A, E, G, Iyy, Izz, J, kappaY, kappaZ

Description

This keyword defines the mechanical and geometric properties of Timoshenko beam elements. The beam properties are specified on a single line with eight parameters.

Parameters

Parameter	Description	Units	Notes
`A`	Cross-sectional area	L² (e.g., m²)	Assumed constant during simulation
`E`	Young's modulus	F/L² (e.g., kPa)	Elastic axial and bending stiffness
`G`	Shear modulus	F/L² (e.g., kPa)	Typically G = E/[2(1+ν)] where ν is Poisson's ratio
`Iyy`	Second moment of area around local y-axis	L\(^4\) (e.g., m\(^4\))	Bending about local y-axis
`Izz`	Second moment of area around local z-axis	L\(^4\) (e.g., m\(^4\))	Bending about local z-axis
`J`	Torsional constant	L\(^4\) (e.g., m\(^4\))	Also known as polar moment of inertia
`kappaY`	Shear correction factor in local y-direction	Dimensionless	Accounts for non-uniform shear stress distribution
`kappaZ`	Shear correction factor in local z-direction	Dimensionless	Accounts for non-uniform shear stress distribution

For 2D simulations, typically only Izz (bending about the out-of-plane axis) and kappaZ are relevant.

Shear Correction Factors

The shear correction factors depend on the cross-sectional shape and account for the non-uniform distribution of shear stresses. Recommended values are provided below:

Cross-Section Type	Configuration	Shear Correction Factor (κ)	Notes
Rectangular	Homogeneous	0.8333 (5/6)	Standard value derived from elasticity theory
I-Sections & IPE Profiles	Strong-axis bending (⊥ to web)	0.3-0.4	Lower values for deeper sections
	Weak-axis bending (∥ to web)	0.5-0.6	Depends on flange width/thickness ratio
Circular	Solid	0.9	Highest κ among common sections
	Thin-walled tube	0.5-0.6	Decreases as wall thickness decreases
Box Sections	Square hollow (thin walls)	0.4-0.5	Higher values for thicker walls
	Rectangular hollow	0.35-0.5	Varies with aspect ratio
Channel Sections	C-shaped (strong-axis)	0.35-0.45	Depends on web/flange proportions
	U-shaped (weak-axis)	0.45-0.55	Higher for more compact sections
T-Sections	All orientations	0.3-0.4	Similar to asymmetric I-sections
Angle Sections	L-shaped	0.45-0.55	Varies with leg length ratio

Examples

Simple Rectangular Beam (2D)

For a rectangular beam with width 0.2 m and height 0.4 m made of concrete (E = 30 GPa, ν = 0.2):

*Beam properties
0.08, 3.0e7, 1.25e7, 0.00107, 0.00107, 0.00167, 0.8333, 0.8333

Where:

A = 0.2 m × 0.4 m = 0.08 m²
E = 30 GPa = 3.0e7 kPa
G = E/[2(1+ν)] = 30/(2×1.2) = 12.5 GPa = 1.25e7 kPa
Iyy = Izz = bh³/12 = 0.2×0.4³/12 = 0.00107 m\(^4\) (assuming same bending capacity in both directions)
J = Iyy + Izz = 0.00167 m\(^4\) (for rectangular section, approximate)
kappaY = kappaZ = 5/6 = 0.8333 (rectangular section)

IPE 200 Steel Beam (3D)

For an IPE 200 steel section (E = 210 GPa, ν = 0.3):

*Beam properties
0.00285, 2.1e8, 8.08e7, 1.94e-5, 1.42e-6, 7.02e-8, 0.4, 0.55