Civil Engineering Reference
In-Depth Information
“ENCASTRE” means fully built-in (fixed case), which implies that the
degrees of freedom 1, 2, 3, 4, 5, and 6 equal to 0. Finally, specifying
“PINNED” means pin-ended case, which implies that the degrees of free-
dom 1, 2, and 3 equal to 0. It should be noted that once a degree of freedom
has been constrained using a type boundary condition as model data, the
constraint cannot be modified by using a boundary condition in direct for-
mat as model data. Also, a displacement-type boundary condition can be used
to apply a prescribed displacement magnitude to a degree of freedom.
All boundary conditions related to the bridge must be carefully applied
and checked that the model has not been overconstrained. Symmetry sur-
faces also require careful treatment to adjust the boundary conditions at the
surface. It should be also noted that applying a boundary condition at a node
to constrain this node from displacing or rotating will totally stop this node
to displace or rotate. When the displacement or rotation is not completely
constrained (partial constraint), springs must be used to apply the boundary
conditions with constraint values depending on the stiffness related to the
degrees of freedom. Different steel bearings briefed in Chapter 3 can be sim-
ulated by either roller or hinged boundary conditions, or they can be mod-
eled using solid elements depending on the loads applied. Further details
regarding the application of loads and boundary conditions in finite element
modeling are found in [ 5.1 ] .
REFERENCES
[5.1] E. Ellobody, F. Ran, B. Young, Finite Element Analysis and Design of Metal
Structures, first ed., Elsevier, 2014, 224 pages, ISBN: 978-0-12-416561-8.
[5.2] E. Ellobody, D. Lam, Finite element analysis of steel-concrete composite girders,
Adv. Struct. Eng. 6 (4) (2003) 267-281.
[5.3] W.H. Bowes, L.T. Russell, Stress Analysis by the Finite Element Method for Prac-
ticing Engineers, Lexington Books, Toronto, 1975.
[5.4] E. Ellobody, C.G. Bailey, Behaviour of unbonded post-tensioned concrete slabs,
Adv. Struct. Eng. 11 (1) (2008) 107-120.
[5.5] A. Hillerborg, M. Modeer, P.E. Petersson, Analysis of crack formation and crack
growth in concrete by means of fracture mechanics and finite elements, Cem. Concr.
Res. 6 (1976) 773-782.
[5.6] J. Lubliner, J. Oliver, S. Oller, E. O˜ate, A plastic-damage model for concrete, Int. J.
Solids Struct. 25 (1989) 299-329.
[5.7] J. Lee, G.L. Fenves, Plastic-damage model for cyclic loading of concrete structures, J.
Eng. Mech. 124 (8) (1998) 892-900.
[5.8] D.W. Murray, E.L. Wilson, Finite element large deflection analysis of plates, Am.
Soc. Civ. Eng. 95 (1) (1969) 143-165.
[5.9] P.G. Bergan, R.W. Clough, Large deflection analysis of plates and shallow shells using
the finite element method, Int. J. Numer. Meth. Eng. 5 (1973) 543-556.
 
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