SPPU Matrix Methods of Structural Analysis - December 2016 Exam Question Paper

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

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 E_st = 210 GPa, E_A1=70 GPa and E_br = 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
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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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