The section material properties need to be defined for a 1 dimensional truss, embedded truss or beam element. Here, the truss and embedded truss only need the cross-sectional area but the beam needs other material properties such as total cross section, torsional rigidity, first area moment of inertia and second area moment of inertia to consider torsion, bend and shear.

The thickness of the element needs to be defined to specify the 2D plane stress element, 2D geogrid element, plate element, plane strain element, axial symmetry element, linear interface element etc. Here, the plane strain element, axial symmetry element and linear interface element have an interior unit weight of 1 and the user can define the used units according to the thickness.

The plane stress element, 2D geogrid element and plate element use the thickness value entered by the user. Here, the plate element has a rotor float and because nonlinear analysis is possible, a separate integration is performed in the thickness direction.

1D element

1D element is an element that is made up of 2(primary) or 3(secondary) nodes and has the geometric property of length. Because 3D shapes are expressed as 1D elements, the section (size, shape) needs to be defined and this is modeled as a 2D element for calculations.

FEA NX provides various shapes, as shown in the figure below. The position can also be set when defining the sectional properties.

<Actual model>                                    <Finite element model>

<Automatic section modeling >

<Section shape and size specification>

2D element

2D elements are Triangles or Quadrilaterals with the geometric property of area. Because 3D shapes are expressed as 2D elements, the thickness needs to be defined. The thickness can be set the same or tapered.

<Actual model>                                 <Finite element model>

3D element

3D elements are Tetrahedron or Hexahedrons, Bricks with the geometric property of volume.

<Actual model>                             <Finite element model>

Cross sectional area (A)

The cross sectional area is used to calculate the axial stiffness when a tensile or axial force acts on the member or the stress on a member. The calculations for the H section are as follows.

There are 2 methods to calculate the cross sectional area in the FEA NX. The first method uses the provided database to input the dimensions of a section and automatically calculate the area. For the second method, the user calculates the area directly and inputs the value. The first method is convenient, but because it does not consider the decrease in area due to bolts in the connection or rivet holes, the area entered using the second method may provide more accurate results.

<Example of cross sectional area calculation>

Torsional stiffness (Ixx)

The torsional stiffness resists the torsional moment and is expressed as follows.

Here,   :  Torsional stiffness,

    :  Torsional moment or torque,

   :  Torsional angle (angle of twist),

   :  Shear modulus

The torsional stiffness is the stiffness that resists the torsional moment and is different from the polar moment of inertia that decides the shear stress due to torsion.  (However, the 2 are the same when considering a circular cross-section or a thick cylindrical section)

The torsional stiffness can be calculated from Saint-Venant's principle as shown below.

  is the warping function that can be calculated using the Finite element method as shown below.

Because , the torsional stiffness comp1nt is expressed as the following equation.

Effective shear area  (Asy, Asz )

The effective shear area is needed to calculate the shear stiffness that resists the shear force acting on the y axis or z axis of the element coordinate system. If the effective shear area is not entered, the shear strain in that direction is ignored.

Here,   :    Effective shear factor that resists shear force in the y axis of the element coordinate system

   :   Effective shear factor that resists shear force in the z axis of the element coordinate system

  :   Effective shear area that resists shear force in the y axis of the element coordinate system

  :   Effective shear area that resists shear force in the z axis of the element coordinate system

When the interior section material properties are calculated or entered from the database, the shear stiffness comp1nt is automatically considered and the effective shear factor is calculated using the warping function from the shear force caused by bending moment and the warping function from the Saint-Venant principle.

Here,

Area moment of inertia (Iyy, Izz)

The area moment of inertia is used to calculate the flexural stiffness that resists the bending moment and is calculated from the centroid axis of the section using the following equation.

• • Area moment of inertia about the y axis of the element coordinate system

• Area moment of inertia about the z axis of the element coordinate system

<Table. First area moment of inertia and calculation of centroid >

  :  area

   :  distance from the reference point to the centroid of the section element in the z′-axis direction

  :  distance from the reference point to the centroid of the section element in the y′-axis direction

   :  first moment of area relative to the reference point in the y′-axis direction

 :  first moment of area relative to the reference point in the z′-axis direction

• • Calculate position of neutral axis  ( , )

• • Calculate second area moment of inertia  ( , )

<Table. Second area moment of inertia example>

Area product moment of inertia  (Iyz)

The area product moment of inertia is used to calculate the stress comp1nt of an asymmetrical section and the definition is as follows.

H, pipe, box, channel, tee type sections have at least 1 axis of symmetry out of the y,z axis on the element coordinate system and hence Iyz=0. For angle type sections, it does not have any angle of symmetry (Iyz≠ 0) and so, the stress comp1nt needs to be calculated.

The calculations for the area product moment of inertia of an angle type section are shown in the figure below.

<Area product moment of inertia calculations for an angle section>

< Flexural stress distribution diagram for asymmetrical section>

The neutral axis is the axis that passes the points where the flexural stress due to the bending moment is ‘0(zero)’ within the member. The neutral axis is perpendicular to the  -axis and the  -axis.

Because the flexural stress due to bending moment is ‘0’ on the neutral axis, the neutral axis direction can be found by the following equation.

The general equation used to calculate the flexural stress due to bending moment is as follows.

If this is a H type section,   and,

Here,  :  Second area moment of inertia about the  axis of the element coordinate system,

 :  Second area moment of inertia about the  axis of the element coordinate system,

 :  Area product moment of inertia,

  :  Elemental  axis distance from neutral axis to where the flexural stress is calculated,

  :  Elemental  axis distance from neutral axis to where the flexural stress is calculated,

:  Bending moment about the  axis of the element coordinate system,

:  Bending moment about the  axis of the element coordinate system

The shear stress due to shear force acting in the  axis and  axis direction of the element coordinate system can be calculated using the following equation.

Here,  :  Shear force acting in the axis direction of the element coordinate system,

 :  Shear force acting in the  axis direction of the element coordinate system,

 :   First area moment of inertia about the axis of the element coordinate system,

 :  First area moment of inertia about the axis of the element coordinate system,

 :  Section thickness at the point where shear stress is calculated in the normal direction to the elemental  axis,

 :  Section thickness at the point where shear stress is calculated in the normal direction to the elemental  axis

First moment of area  (Qy, Qz)

The first moment of area is used to calculate the shear stress at an arbitrary point on the section and the shear stress can be calculated using the following equation.

For a section that is symmetrical about the y, z or both axis, the shear strength on an arbitrary point can be calculated using the following equation.

Here,  :  Shear force acting in the axis direction of the element coordinate system,

 :  Shear force acting in the axis direction of the element coordinate system,

 :  Second area moment of inertia about the axis of the element coordinate system,

 :  Second area moment of inertia about the axis of the element coordinate system,

 :  Section thickness at the point where shear stress is calculated in the normal direction to the elemental  axis,

 :   Section thickness at the point where shear stress is calculated in the normal direction to the elemental  axis

Element thickness

On the FEA NX, the thickness needs to be defined to specify the 2D plane stress element, 2D geogrid element, plate element, plane strain element, axial symmetry element, linear interface element etc. Here, the plane strain element, axial symmetry element and linear interface element have an interior unit weight of 1.

The plane stress element, 2D geogrid element and plate element use the thickness value entered by the user. The plate element has a rotor float and because nonlinear analysis is possible, a separate integration is performed in the thickness direction.

Spacing

This functionality is in the 1D element property which is activated only in 2D project setting. Since this option is used to consider the 1D element force per each element when the user introduce the 1D element more or less than one along the axis of horizontal direction (thickness direction) in 2D model.

If the user uncheck the spacing option, on the FEA NX, the spacing will be regarded as Plane Strain Thickness in the analysis setting, meaning that the unit thickness based on the selected unit system.

On the FEA NX, spacing is used to calculate the stiffness of the element and output the member force per each element.

where, n = spacing, L = length , A = area, K* = stiffness considering spacing.

where, f* = member force

Refer to the following example,