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SPPU Civil Engineering (Semester 7)
Matrix Methods of Structural Analysis
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

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Solve any one question fromQ.1(a,b,c) and Q.2(a,b,c)
1(a) Solve the following system by Gauss-Jordan Method
x+y+z
2x+3y+5z=8
4x+5z=2
6 M
1(b) Analyse the beam ABC shown in Figure 1 using flexibility matrix method. AB = 3 m and BC = 6 m. Take EI = constant
!mage
6 M
1(c) A rod is composed of an aluminum section rigidly attached between steel and bronze as shown in Figure 2. If the cross-section area of rod is 800 mm2 determine nodal displacements. Take Est = 210 GPa, EA1=70 GPa and Ebr = 110 Gpa.
!mage
8 M

2(a) Solve the following system by Gauss- Elimination Method
x+y+z
2x+3y+5z=8
4x+5z=2
6 M
2(b) Find the vertical and horiziontal deflection point C for the two member truss as shown in Figure 3. Area of inclined member is 2000 mm2 where as horizontal members is 16000 mm2. Take E = 200 Gpa
!mage
6 M
2(c) Analyse the beam ABC shown in Figure 4 using flexibility matrix method. Take EI = constant.
!mage.
8 M

Solve any one question fromQ.3 and Q.4
3 Analyze the continous beam ABCD shown in Figure 5 using stiffness matrix method. Take EI constant. Draw BMD
!mage.
18 M

4 Determine the unknown joint diplacements of the portal frame as shown in Figure 6 using stiffness matrix method. Take EI constant.
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18 M

Solve any one question fromQ.5 and Q.6
5 Derive the stiffness matrix and transformation matrix of two noded grid element of with 06 D. O. F., length L, flexural rigidity EI and torsional rigidity GJ.
16 M

6 Analyze the grid structure ABC is shown in Figure 7 using stiffness matrix method Take EI = 2×105kN.m2 and GJ = 1.2×105kN.m2.
!mage
16 M

Solve any one question fromQ.7 and Q.8(a,b)
7 For the truss shown in Figure 7, use stiffness matrix method to determine the deflections at the loaded joint. Take E = 200 GPa and c/s area of all members 1000 mm2
!mage
16 M

8(a) A beam of span '8m' is fixed at both ends 'A' and 'B' and supports a unifomly distributed load of 10kN/m over the entire span. Estimate the deflections of quarter span intervals using second order central difference formula.
!mage
8 M
8(b) Estimate the lowest buckling load 'P' of a uniform pin ended column of length 'L = 10m', cross-sectional area 100×100 mm and E = 200 GPa using three sub intervals .Apply finite difference method.
8 M


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