SPPU Civil Engineering (Semester 8)
Finite Element Method in Civil Engineering
December 2016
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question fromQ.1(a,b,c) and Q.2(a,b,c)
1(a) Write short note on:
i) Discretization of structure
ii) Aspect ratio of element
6 M
1(b) Determine displacement at loaded joint of truss shown in figure using finite element method Take A = 1000 mm@ and E = 200 GPa
8 M
1(c) Derive the transformation matrix for two noded frame element having six degrees of the freedom.
6 M

2(a) State the convergence criteria for the choice of the displacement function in FEM.
6 M
2(b) Determine rotations at supports B and C of continuous beam ABC if support B sinks by 10mm. Take EI = 6000kN.m2.Use finite element method.
8 M
2(c) Deriev the stiffness matrix for th r grid element six degrees of freedom.
6 M

Solve any one question fromQ.3 and Q.4
3 Write short note on:
a) Principle of minimum potential energy
b) Principle of virtual work
c) CST and LST elements
d) 3D Tetrahedron and Hexahedron elements.
16 M

4 Derive connectivity matrix [A], elasticity matrix [D], strain-displacement matrix [B] and stiffness matrix [K] for the four noded rectangular element in Cartesian coordinate system using finite element formulation.
16 M

Solve any one question fromQ.5(a,b,c) and Q.6(a,b)
5(a) Deriev shape functions for the following elements using Lagrange's interpolation function
Two noded bar element
4 M
5(b) Four noded rectangular element
6 M
5(c) Nine noded rectangular element
8 M

6(a) Derive the area coordinates for the three noded CST element having Cartesian coordinates node 1 (1,2), node 2 (3,3) and node 3 (2,4).
10 M
6(b) Derive shape functions for the eight noded serendipity element in natural coordinate (ξ,η) system.
8 M

Solve any one question fromQ.7(a,b,c) and Q.8
7(a) Write short note on:
i) Isoparametric, sub-parametric and super-parametric elements
5 M
7(b) Theorems of isoparametric formulations
5 M
7(c) Jacobian matrix
6 M

8 Derive the Jacobian matrix for the four noded quadrilateral isoparametric element having Cartesian coordinates at node 1 (1,1), node 2 (4,1), node 2 (1,2) and node 4 (4,2).
16 M

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