Results Interpretation: Result Quantities

Translations and rotations of a node. For example, D(X), D(Y), D(Z), R(X), R(Y), R(Z) are translations in and rotations about the first, second and third axis respectively of either the global or the user-defined coordinate system (UCS). Magnitudes of resultant vectors are also available, for example:

In Results: Peek and The LISTINGS Tab, original node coordinates before displacement in global XYZ or UCS (e.g., X, Y, Z), and the coordinates after displacement (e.g., X', Y', Z'), are also given for reference. For example:

If a reference Ref. Node is specified, the displacement is calculated relative to the displacement of the reference node. These are calculated as 'displacements at point' minus 'displacements at reference node'. For example, if relative quantities are requested, these are calculated as minus , not the of the difference in and of the respective points. That is:

External force and moment reactions at a restrained or supported node. For example, F(X) and M(X) are force reaction in, and moment reaction about, the X axis respectively. Magnitude of resultant vectors are available and are derived similarly to those of Node Displacement.

Node reactions can be reported in the Global system, UCS or Restraint UCS. Node reactions of brick elements can also be reported in the brick's local axes. Restraint UCS refers to the UCS of the restraint attribute applied to the node, in the current results case and in the 1-2-3 system (i.e., the first, second and third axis of the UCS).

Similarly to Node Reaction, element node forces are free body forces and moments at a node that balance the element's internal forces and moments, irrespective of whether the node is restrained or not.

Similarly to Node Reaction, link node forces are the sum of Element Node Force results produced by the elements connected to the link node. For Reaction MPLs, the forces are the sum of the results contributed by the connected elements contained in the Entity Set referenced by the MPL.

Phase angles of the node translations and rotations in degrees, available for Harmonic Response results. For example, P(X) and PR(X) are phase angles in and about the X axis respectively. Magnitude of resultant vectors are available and are derived similarly to those of Node Displacement. See Solvers Background: Harmonic Response.

The rate of heat flow per unit area. Positive value means that the heat energy flows in the same direction as the selected axis while negative value indicates that the heat energy flows in the opposite direction. For beam elements, the axis is the beam's principal 3 axis (see Beam Elements: Local and Principal Axes). For plate and brick elements, the axis can be a local x, y, z axis, a global axis or a user-defined coordinate system (UCS) axis (see Plate Elements: Local Axes and Brick Elements: Local Axes). Magnitude calculation is similar to that of Node Displacement.

Difference in temperature per unit length in a selected axis. Positive value means temperature is increasing along the axis while negative value indicates that the temperature is decreasing along the axis. For beam elements, the axis is the beam's principal 3 axis (see Beam Elements: Local and Principal Axes). For plate and brick elements, the axis can be a local x, y, z axis, a global axis or a user-defined coordinate system (UCS) axis (se Plate Elements: Local Axes and Brick Elements: Local Axes). Magnitude calculation is similar to that of Node Displacement.

The summation of forces and moments of linked nodes about the origin of the Reaction multi-point link. See Entities: Links.

Internal forces of a beam element with reference to its local, principal, global or a user-defined coordinate system at the beam ends. Internal forces includes:

• Bending moments
• Transverse Shear forces
• Axial force
• Torque

See Results Interpretation: Beam Force and Moment Conventions.

Axial force experienced by a beam element per its cross section area at that point:

Fibre stress on the cross section of a beam element due to pure bending moments in the principal planes. Note that positive bending moment produces compressive (i.e., negative), stress in fibres above the centroid.

• Plane 1: 

  

  where is the bending moment in plane 1, is the second moment of area about principal 2 axis and is the projected distance in the principal 1 axis from section centroid to a point on the cross section.

• Plane 2:

  

  where is the bending moment in plane 2, is the second moment of area about principal 1 axis and is the projected distance in the principal 2 axis from section centroid to a point on the cross section.

Total stress of a fibre on the cross section of a beam due to bending moments and axial force. Shear actions are excluded. Beam section shape must be defined for stresses to be calculated.

Similar to Beam Fibre Stress, fibre strain is the axial displacements of a fibre as a ratio of its initial or current length due to bending moments and axial force. See Results Interpretation: Total, Deformation, Nominal and Engineering Strain.

Catenary cable element is an exception of which the fibre strain is defined as:

where

= mechanical or total strain in the cable,

= position along the cable,

= deformational strain at ,

= axial force at ,

= cable cross section area,

= Young’s modulus,

= cable free length (for cables without the free length attribute, is equal to the initial distance between the nodes),

= initial cable length (that is, the stress-free length of the cable) ,

= uniform thermal (engineering) strain along cable length (due to node temperature attributes), and

= (engineering) pre-strain (due to pre-strain attributes) uniform along the cable length.

See also Results Interpretation: Total, Deformation, Nominal and Engineering Strain.

Stress that is parallel to the cross section and at a point on the cross section of a beam element.

• due to Shear Force 1:

  Transverse shear stress in the principal plane 1 that is caused by only the component of shear force in the principal 1 axis.

• due to Shear Force 2:

  Transverse shear stress in the principal plane 2 that is caused by only the component of shear force in the principal 2 axis.

• due to Torque:

  Shear stress that is caused by only the torque about the principal 3 axis.

• Plane 1:

  Transverse shear stress in the principal plane 1 that is caused by the applied load.

• Plane 2:

  Transverse shear stress in the principal plane 2 that is caused by the applied load.

• Magnitude Plane 1-2:

  The magnitude of the transverse shear stress in both principal plane 1 and 2 combined that is caused by the applied load.

• Mean Shear Stress due to Shear Force 1:

  The shear force in the principal 1 axis divided by the cross section area.

• Mean Shear Stress due to Shear Force 2:

  The shear force in the principal 2 axis divided by the cross section area.

The ratio of cross section area that has yielded. For example, a value of 0.75 means that 75% of the cross section area at that particular station along the beam has yielded.

For bending elements (for example, Beam Properties: Beam type elements), the yield ratio is between 0.0 and 1.0. For non-bending elements (for example, Beam Properties: Truss type elements), the yield ratio is either 0.0 or 1.0. For beams with Moment-Curvature and Axial Stress vs Strain tables, where each of the bending and the axial directions can yield independently, the yield ratio can be one of 0/3, 1/3, 2/3, 3/3, where the numerator refers to the number of axes that have yielded (e.g., 2/3 could mean that it has yielded about one of the axes and in the axial direction). The same convention is adopted for Beam Properties: Connection type elements which can have up to six different tables (hence valid yield ratios are 0/6, 1/6 … 6/6).

The average of the three normal stress or strain components. Also known as the hydrostatic or volumetric part of a stress tensor. See Results Interpretation: Stress Conventions.

The difference between the mean stress and the three normal stress components. See Results Interpretation: Stress Conventions.

Principal stresses are normal stresses in an axis system in which shear stresses are all zero. The most positive principal stress is denoted , followed by and (i.e., ). The corresponding axes in which these principal stresses act are called principal axes.

For beam elements, the principal stress combines the fibre stress and shear stresses due to torque and transverse shear forces.

Similarly for principal strains.

An effective stress according to the following equation:

Similarly for von Mises strain.

An effective stress according to the following equation:

Similarly for Tresca strain.

The principal stress with the largest magnitude.

Similarly for Max Magnitude strain.

An indicator according to the Mohr-Coulomb yield criterion. The value is a stress difference; that is, a measure of how far a stress point is from the yield surface. Positive value indicates that the material stress state is outside the yield surface (i.e., material failure).

where

= material cohesion, and

= material internal friction angle.

An indicator according to the Drucker-Prager yield criterion that combines the Mohr-Coulomb and von Mises criteria. The value is a stress difference; that is, a measure of how far a stress point is from the yield surface. Positive value indicates that the material stress state is outside the yield surface (i.e., material failure).

where

= material cohesion

= material internal friction angle

Strain energy per length of beam element, per area of plate element, or per volume of brick element, due to element strain and deformation. Note that this result quantity does not include the kinetic energy of the element in transient dynamic analysis.

• Spent Energy:

  The total energy used to stretch and deform the element to its current shape.

• Stored Energy:

  The recoverable energy if the element is unloaded. If the element has not yielded, the stored energy is equal to spent energy. If the material is nonlinear elastic, the stored energy is equal to the spend energy. If an elasto-plastic element has yielded, the stored energy is equal to the elastic energy that is recoverable upon unloading.

  

Element Strain must be included in the results file for energy results to be calculated.

This is the integral of Energy Density results. Energy integral is given as a single value per element, in absolute energy units such as Joules.

Element Strain must be included in the results file for energy results to be calculated.

The positions along the cable element in the global XYZ system. Positions at up to 20 slices are available.

This results quantity is only available in Results: Peek and The LISTINGS Tab.

Plate element's normal forces, in-plane shear force and transverse shear forces expressed in either the local x, y, z axes, the global axes or the axes of a user-defined coordinate system (UCS) (see Plate Elements: Local Axes). Similarly to stresses, plate element forces can be transformed to the principal axes and combined. See Results Interpretation: Plate Shear Force and Moment Conventions.

Plate element's bending moments expressed in either the local x, y, z axes, the global axes or the axes of a user-defined coordinate system (UCS) (see Plate Elements: Local Axes). Similarly to stresses, plate element bending moments can be transformed to the principal axes and combined. See Results Interpretation: Plate Shear Force and Moment Conventions.

Shows both the plate element force and bending moment results on the same page. This also applies to Results Interpretation: Expanded Envelope Results to determine equilibrated force and moment components for a given envelope value.

Normal and shear stresses of the ply material that forms the laminate stack.

• Fibre 11:

  Stress in the ply fibre 1 direction.

• Fibre 22:

  Stress in the ply fibre 2 direction.

• Fibre 12:

  In-plane shear stress of the ply.

• Interlamina Shear x:

  Interlamina shear stress in the local element x direction.

• Interlamina Shear y:

  Interlamina shear stress in the local element y direction.

• von Mises stress
• Tresca stress

Interlamina shear is reported in between the plies and is zero at the outermost surfaces of the laminate. For example, the interlamina shear reported for Ply 1 is the shear stress at the top of Ply 1 (i.e., at the interface between Ply 1 and Ply 2).

As with other stress quantities, ply stresses can be transformed to the principal axes and combined. See Results Interpretation: Stress Conventions.

Similarly for Composite Ply Strain.

Reserve factor is generally a ratio between the allowable load at failure of the ply material and its current applied load, i.e.:

The ply is considered safe if the reserve factor is greater than 1. The allowable load at failure is defined under LAYOUTS: Plies.

• Maximum Stress:

  Directly compares the maximum ply stress in Fibre 11, Fibre 22 and Fibre 12 with the respective allowable tensile, compressive and in-plane shear stress and shows the lowest reserve factor. That is,

  where , , are the allowable stresses in the fibre 1, 2 and in-plane shear respectively. is the tensile limit if the corresponding ply stress is positive and compressive limit if the corresponding ply stress is negative.

• Maximum Strain:

  Similarly to Maximum Stress, directly compares the maximum ply strain in Fibre 11, Fibre 22 and Fibre 12 with the respective allowable tensile, compressive and in-plane shear strains. That is,

  where , , are the allowable strains in the fibre 1, 2 and in-plane shear respectively. is the tensile limit if the corresponding ply strain is positive and compressive limit if the corresponding ply strain is negative.

• Tsai-Hill:

  Also known as the maximum work theory, one of three quadratic failure criteria that calculates the failure index as:

  

  The ply is considered safe if the failure index is less than 1. The reserve factor is calculated as:

  

• Hoffman:

  One of three quadratic failure criteria that calculates the failure index as:

  

  

  The ply is considered safe if the failure index is less than 1. The reserve factor is calculated as:

  

• Modified Tsai-Wu:

  One of three quadratic failure criteria that calculates the failure index as:

  

  where , , , and are the same as those of the Hoffman criterion above.

  

  is the interaction coefficient obtained from the determination of ply strength under equal biaxial tensile loading and is taken as zero in Strand7. The ply is considered safe if the failure index is less than 1. The reserve factor is calculated as:

  

• Interlamina Shear Stress:

  Directly compares the maximum interlamina shear stress in the x and y directions with the respective allowable interlamina shear stress and shows the lowest reserve factor.

  where is the allowable interlamina shear stress.

  This criterion is based on a relatively simple beam theory and is used to predict the failure between plies due to shearing actions.

Quantities include:

• Wood-Armer forces and moments
• Steel Areas, Bar Sizes and Spacings
• Concrete Strain
• Concrete Block Ratio
• User Steel Stress
• User Concrete Strain

See Results Interpretation: Plate RC.

Soil stress excluding pore pressure.

Soil stress including pore pressure.

The total pore pressure, which includes the initial and the excess pore pressures.

Pressure built up inside the void of undrained soil material as the material compacts and deforms. Additional pressure can build up when liquid within the void is confined from flowing freely when the external load changes.

Pore pressure is available for undrained soil only.

Over Consolidation Ratio is the ratio of the past effective pressure (pre-consolidation pressure) to the current overburden pressure. A normally consolidated soil has OCR=1, an over-consolidated soil has OCR>1.

OCR is available for Modified Cam-Clay Soil only.

State index ranges from -1 to +1. A negative value of state index indicates that the soil p-q state is below the critical state line; a positive value of state index indicates that the soil p-q state is above the critical state line. The state index approaches the critical state line as it increases.

State index is available for Modified Cam-Clay Soil only.