Gujarat Technological University 2010-1st Sem M.E Computer Aided Design Redial - Question Paper
GUJARAT TECHNOLOGICAL UNIVERSITY
M.E Sem-I Remedial exam April 2010
Subject code: 711501
Subject ame: Matrix Analysis of Framed Structure
Date: 06 / 04 /2010 Time: 12.00 noon – 03.00 pm
Total Marks: 60
Seat No. Enrolment No.
GUJARAT TECHNOLOGICAL UNIVERSITY
M.E Sem-I Remedial Examination April 2010 Subject code: 711501
Subject Name: Matrix Analysis of Framed Structure Date: 06 / 04 /2010 Time: 12.00 noon - 03.00 pm
Total Marks: 60
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Take E=200 GPa, G=80 GPa, EI=200x103 kN.m2 and GJ=0.8EI, if not specified in any problem.
Q.1 (a) For the beam shown in fig.-1, the rotation at joint B and joint C is found 06 to be 36.16/EI (anticlockwise) & -4.02/EI (clockwise) respectively for the given loading. Find out internal forces in the member using Stiffness method and plot diagrams.
(b) Derive assembled flexibility matrix for the beam shown in fig.-1 considering 06 moment at A and B are redundant.
Q.2 (a) Find out displacement of a plane truss shown in fig.-2 considering symmetry 06 of structure by Stiffness method.
(b) Derive load vector of the plane frame shown in fig.-3(a) & 3(b) 06
OR
(b) Derive the relation to transfer actions/displacement from member axes to 06 structure axes or vice versa. Using same relation, find out axial, transverse & bending deformation of the member BC for fig.-3(a), if displacement found at rigid joint is Sx = 4.146/EI, Sy = -1.762/EI & 9z =-3.011/EI (clockwise).
Take I/A=1/100.
Q.3 (a) For the plane frame shown in fig.-3(b), derive complete joint stiffness matrix 06 showing partitioning and load vector. Take I/A=1/100.
(b) Compute displacements and member end actions for the plane frame shown 06 in fig.-3(b). Plot deflected shape and member end actions diagrams also.
OR
Q.3 (a) For the plane frame shown in fig.-4 has constant EI for all members. Find out 06 necessary matrices to derive assembled flexibility matrix. You may choose your own sets of redundant.
(b) Calculate displacements at joints, reactions and member end actions for the 06 plane frame shown in fig.-4 using Flexibility member approach. Plot all necessary diagrams.
Q.4 (a) Derive joint stiffness matrix and load vector for the Grid shown in fig.-5 06 considering symmetry of the structure.
(b) Compute displacements and member end actions for the Grid shown in fig.- 06
5. Plot deflected shape and member end actions diagrams also.
OR
Q.4 (a) Explain the derivation of flexibility matrix FM, BMS matrix, BRS matrix and assembled flexibility matrix FS with partitioning for the plane truss structure. Also explain how to find out displacements, reactions and member end actions.
(b) Compute displacements and member end actions for the space truss shown in fig.-6 considering symmetry of the structure. Take axial rigidity of member AD is 30 MN and for member AB and AC is 20 MN.
06
Q.5 (a) A composite structure shown in fig.-7 consist of a beam ABC made of a 06 concrete of grade M20 and having size of 250 mm x 450 mm, which
supported by a steel rod of 20 mm diameter at centre of its length. Take
1/2
Econcrete = 5000(fck) and Esteel=200 GPa. Determine joint stiffness matrix and load vector of the structure considering symmetry of the structure.
(b) Compute displacement, reactions and member end actions of the composite 06 structure shown in fig.-7. Plot structural response neatly.
OR
Q.5 (a) In a plane truss shown in fig.-2, member CD is found to be 5 mm shorter 06 than its original length. How this effect can be incorporated in the analysis by Stiffness method? Show necessary calculations.
(i) support B sinks by 10 mm and
(ii) it is subjected to temperature variation of 40 at top and 15 at bottom of the beam
in addition to the load given on it.
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