Truss2 Element: Difference between revisions

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This command is used to construct a Truss2 or CorotTruss2 element object, a biaxial truss element designed to be used in conjunction with the [[ConcretewBeta Material| ConcretewBeta]] Material for accounting for biaxial effects in a uniaxial element.
This command is used to construct a Truss2 or CorotTruss2 element object, a biaxial truss element designed to be used in conjunction with the '''[[ConcretewBeta Material| ConcretewBeta]]''' material for accounting for biaxial effects in a uniaxial element.


Truss:
Truss:
{|  
{|  
| style="background:yellow; color:black; width:800px" | '''element Truss2 $tag $iNode $jNode $auxN1 $auxN2 $A $matTag <-rho $rho> <-rayleigh $rflag>'''
| style="background:yellow; color:black; width:800px" | '''element Truss2 $eleTag $iNode $jNode $mGNode $nGNode $A $matTag <-rho $rho> <-rayleigh $rflag>'''
|}
|}


Corotational Truss:
Corotational Truss:
{|  
{|  
| style="background:yellow; color:black; width:800px" | '''element CorotTruss2 $eleTag $iNode $jNode $auxN1 $auxN2 $A $matTag <-rho $rho>'''
| style="background:yellow; color:black; width:800px" | '''element CorotTruss2 $eleTag $iNode $jNode $mGNode $nGNode $A $matTag <-rho $rho>'''
|}
|}


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| Optional:
| Optional:
|-
|-
| '''$rho''' || mass per unit length, as in the [[Truss Element| Truss]] and [[Corotational Truss Element| corotTruss]] Elements (default = 0.0)
| '''$rho''' || mass per unit length, as in the '''[[Truss Element| Truss]]''' and '''[[Corotational Truss Element| CorotTruss]]''' Elements (default = 0.0)
|-
|-
| '''$rFlag''' || flag for Rayleigh damping, as in the [[Truss Element| Truss]] Element (default = 0; see Note 2)
| '''$rFlag''' || flag for Rayleigh damping, as in the '''[[Truss Element| Truss]]''' Element (default = 0; see Note 2)
|}
|}


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NOTES:
NOTES:


(1) If the material used does not use biaxial effects, the element will behave like the uniaxial counterpart ([[Truss Element|Truss]] or [[Corotational Truss Element| CorotTruss]]). For the [[ConcretewBeta Material| ConcretewBeta]] material, the normal strain will be passed to the material to be used in calculation of the material response.
(1) If the material used does not use biaxial effects, the element will behave like the uniaxial counterpart ('''[[Truss Element|Truss]]''' or '''[[Corotational Truss Element| CorotTruss]]'''). For the '''[[ConcretewBeta Material| ConcretewBeta]]''' material, the normal strain will be passed to the material to be used in calculation of the material response.


(2) Consistent with the implementation of the [[Truss Element| Truss]] element, the Truss2 element does not include Rayleigh damping by default. Rayleigh damping can be included by using the -rayleigh option with '''$rFlag''' = 1.  
(2) Consistent with the implementation of the '''[[Truss Element| Truss]]''' element, the Truss2 element does not include Rayleigh damping by default. Rayleigh damping can be included by using the -rayleigh option with '''$rFlag''' = 1.  


However, like the [[Corotational Truss Element| CorotTruss]] element, the CorotTruss2 element includes the Rayleigh damping by default so the -rayleigh option is not available to the CorotTruss2 element.
However, like the '''[[Corotational Truss Element| CorotTruss]]''' element, the CorotTruss2 element includes the Rayleigh damping by default so the -rayleigh option is not available to the CorotTruss2 element.


(3) At this time, there is no trussSection equivalent implementation of these biaxial trusses.
(3) At this time, there is no trussSection equivalent implementation of these biaxial trusses.
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==Implementation==
==Implementation==


::[[File:Truss2_Fig1.png|thumb|center|upright=2.5|alt=Truss2 Figure 1 |Figure 1. Truss2 truss and gauge element layout based on input node values.]]
::[[File:Truss2_Eq1.png|thumb|upright=1.5|Equation 1.]]


The above figure shows the layout of the truss and zero-stiffness gauge elements that make up the Truss2 Element object. The truss element part behaves identically to the [[Truss Element| Truss]] Element object (or the [[Corotational Truss Element| CorotTruss]] Element object for the case of CorotTruss2).  
The above figure shows the layout of the truss and zero-stiffness gauge elements that make up the Truss2 Element object. The truss element part behaves identically to the '''[[Truss Element| Truss]]''' Element object (or the '''[[Corotational Truss Element| CorotTruss]]''' Element object for the case of CorotTruss2).  


The zero-stiffness gauge element is used to measure the strain in the direction of the gauge. The strain in the direction normal to the truss element is calculated as:
The zero-stiffness gauge element is used to measure the strain in the direction of the gauge. The strain in the direction normal to the truss element is described by Equation 1, where ''&epsilon;<sub>truss</sub>'' is the strain calculated in the truss element, ''&epsilon;<sub>gauge</sub>'' is the strain calculated in the gauge element, and ''&theta;<sub>g</sub>'' is the angle between the truss and gauge elements. It is suggested to make ''&theta;<sub>g</sub>'' as close to 90&deg; as possible.  
::[[File:Truss2_Eq1.png|thumb|center|upright=1.8|Equation 2.]]
where ''&epsilon;<sub>truss</sub>'' is the strain calculated in the truss element, ''&epsilon;<sub>gauge</sub>'' is the strain calculated in the gauge element, and ''&theta;<sub>g</sub>'' is the angle between the truss and gauge elements. It is suggested to make ''&theta;<sub>g</sub>'' as close to 90&deg; as possible.  


::[[File:Truss2_Fig1.png|thumb|center|upright=2.5|alt=Truss2 Figure 1 |Figure 1. Truss2 truss and gauge element layout based on input node values.]]


==References==
==References==

Latest revision as of 01:42, 7 September 2013

This command is used to construct a Truss2 or CorotTruss2 element object, a biaxial truss element designed to be used in conjunction with the ConcretewBeta material for accounting for biaxial effects in a uniaxial element.

Truss:

element Truss2 $eleTag $iNode $jNode $mGNode $nGNode $A $matTag <-rho $rho> <-rayleigh $rflag>

Corotational Truss:

element CorotTruss2 $eleTag $iNode $jNode $mGNode $nGNode $A $matTag <-rho $rho>
$eleTag unique element object tag
$iNode $jNode end nodes of the truss element
$mGNode $nGNode end nodes for the zero-stiffness gauge element
$A cross-sectional area of truss element
$matTag tag of material used (see Note 1)
Optional:
$rho mass per unit length, as in the Truss and CorotTruss Elements (default = 0.0)
$rFlag flag for Rayleigh damping, as in the Truss Element (default = 0; see Note 2)


NOTES:

(1) If the material used does not use biaxial effects, the element will behave like the uniaxial counterpart (Truss or CorotTruss). For the ConcretewBeta material, the normal strain will be passed to the material to be used in calculation of the material response.

(2) Consistent with the implementation of the Truss element, the Truss2 element does not include Rayleigh damping by default. Rayleigh damping can be included by using the -rayleigh option with $rFlag = 1.

However, like the CorotTruss element, the CorotTruss2 element includes the Rayleigh damping by default so the -rayleigh option is not available to the CorotTruss2 element.

(3) At this time, there is no trussSection equivalent implementation of these biaxial trusses.


Implementation

Equation 1.

The above figure shows the layout of the truss and zero-stiffness gauge elements that make up the Truss2 Element object. The truss element part behaves identically to the Truss Element object (or the CorotTruss Element object for the case of CorotTruss2).

The zero-stiffness gauge element is used to measure the strain in the direction of the gauge. The strain in the direction normal to the truss element is described by Equation 1, where εtruss is the strain calculated in the truss element, εgauge is the strain calculated in the gauge element, and θg is the angle between the truss and gauge elements. It is suggested to make θg as close to 90° as possible.

Truss2 Figure 1
Figure 1. Truss2 truss and gauge element layout based on input node values.

References

Lu, Y., and Panagiotou, M. (2013). “Three-Dimensional Nonlinear Cyclic Beam-Truss Model for Reinforced Concrete Non-Planar Walls.” Journal of Structural Engineering, published online.

Panagiotou, M., Restrepo, J.I., Schoettler, M., and Kim G. (2012). "Nonlinear cyclic truss model for reinforced concrete walls." ACI Structural Journal, 109(2), 205-214.


Code Developed by: Yuan Lu, UC Berkeley and Marios Panagiotou, UC Berkeley

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