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14.3. BEAM3 - 2-D Elastic Beam
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Theory Reference > Chapter 14. Element Library >14.3. BEAM3 - 2-D Elastic Beam
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14.3. BEAM3 - 2-D Elastic Beam
Matrix or Vector
Shape Functions
Integration
Points
Stiffness and Mass Matrices; and Thermal and Pressure
Load Vector
Equation 12.4 and Equation
12.5
None
Stress Stiffness Matrix
Equation 12.5
None
Load Type Distribution
Element Temperature Linear thru thickness and along length
Nodal Temperature Constant thru thickness, linear along length
Pressure
Linear along length
Element Matrices and Load Vectors
The element stiffness matrix in element coordinates is (Przemieniecki( 28 )):
Equation 14.1.
mk:@MSITStore:C:\Moje%20dokumenty\MKB\Ansys\ansyshelp.chm::/thy_el3.html
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14.3. BEAM3 - 2-D Elastic Beam
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where:
A = cross-section area (input as AREA on R command)
E = Young's modulus (input as EX on MP command)
L = element length
I = moment of inertia (input as IZZ on R command)
G = shear modulus (input as GXY on MP command)
F s = shear deflection constant (input as SHEARZ on R command)
The consistent element mass matrix ( LUMPM ,OFF) in element coordinates is (Yokoyama( 167 )):
Equation 14.2.
where:
ρ = density (input as DENS on MP command)
m = added mass per unit length (input as ADDMAS on R command)
ε in = prestrain (input as ISTRN on R command)
mk:@MSITStore:C:\Moje%20dokumenty\MKB\Ansys\ansyshelp.chm::/thy_el3.html
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14.3. BEAM3 - 2-D Elastic Beam
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The lumped element mass matrix ( LUMPM ,ON) in element coordinates is:
Equation 14.3.
The element pressure load vector in element coordinates is:
Equation 14.4.
For uniform lateral pressure,
Equation 14.5.
Equation 14.6.
mk:@MSITStore:C:\Moje%20dokumenty\MKB\Ansys\ansyshelp.chm::/thy_el3.html
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14.3. BEAM3 - 2-D Elastic Beam
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Equation 14.7.
where:
P = uniform applied pressure (units = force/length) (input on SFE command)
Other standard formulas (Roark( 48 )) for P 1 through P 6 are used for linearly varying loads, partially
loaded elements, and point loads.
Stress Calculation
The centroidal stress at end i is:
Equation 14.8.
where:
F x,i = axial force (output as FORCE)
The bending stress is
Equation 14.9.
where:
M i = moment at end i
t = thickness of beam in element y direction (input as HEIGHT on R command)
The presumption has been made that the cross-section is symmetric.
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14.2. PLANE2 - 2-D 6-Node Triangular
Structural Solid
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14.4. BEAM4 - 3-D Elastic Beam
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