BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
HYDERABAD CAMPUS
Course: (CE G617) Advanced Structural Analysis FIRST SEMESTER 2015-2016
Maximum Marks: 60 Date: 03.12.2015
Max Duration: Part I - 120 Min , Part II – 60 Min Component Weightage: 30%
Comprehensive Exam (Closed book)
PART – I
Note: 1. Answer all questions.
2. Non programmable scientific calculators are allowed.
3. Use of Mobiles / electronic gadgets is strictly prohibited.
4. Notations used are standard and will have their usual meaning.
5. Assume any suitable data, if necessary.
1. Analyze the structure with combination of beam and steel rod as shown in Figure 1 using direct
stiffness method. The beam has EI= 1.44×104 KN-m2 and is inextensible. The steel rod has EA=
1.25×104 KN. (08 marks )
Figure 2
Figure 1
2. Find the bar forces for all members in the plane truss in Figure 2. Assume all bars to have equal axial
rigidity EA. If the bars are force-fitted due to bar ‘2’ being short by 5mm (fabrication error).
Also include the effect of the applied loads F1=50 kN and F2=225 kN. Use the Flexibility method,
(08 marks)
3. Use the Direct Stiffness Method to analyze the structure shown in Figure 3. However, replace the L-
shaped bracket with load P with its equivalent loads at the midspan of member a-b. E is uniform, and
the relative values of I are shown in Figure. Neglect all axial deformations, i.e., assume that all
members are axially inextensible. What are the unknown nodal displacements for this problem? Set
up the stiffness equations {P} = [K] {Δ} for these free degrees of freedom but do NOT solve these for
the displacements. (08 marks )
4. Analyse the frame shown in Figure 4 using Displacement transformation method for displacements
(08 marks )
L/4
P Figure 3
L/4
b Figure 4
a 4I 2I c
20 kN-m 30 kN-m
3I P/L L 4m
(2I)
4m 4m
(I) (I)
d
L/2 L/2 L
5. Answer the following:
a) Discuss the approach used in matrix method of analysis of structures to apply body or surface
loads (such as spread load to a beam, plane frame, etc.) (2 marks )
b) Discuss the approach used in matrix method of analysis of structures with inclined roller
supports (2 marks )
c) Obtain the horizontal deflection at top of the shear wall shown in Figure 5. You may directly
solve for only horizontal deflection at top using the basics you know. Or you may make use of
the following element stiffness / flexibility for shear wall element given below. Use proper load
vector and boundary conditions depending on the shear element you choose. (4 marks )
W
Figure 5
Flexibility Matrix Stiffness matrix ar = shear area
Shear wall element with two d.o.f.
Stiffness matrix
Shear wall element with four d.o.f.
PART – II
Note: 1. Answer all questions.
2. Matlab programs for beam, framed structures and programmable device (computers) are allowed.
3. Use of Mobiles and internet are strictly prohibited.
4. Notations used are standard and will have their usual meaning.
5. Assume any suitable data, if necessary.
6. Write the steps and the results in the answer sheets
6. Figure 6 shows two identical horizontal beams, AB and CD, at right angles to each other in plan, and
monolithically connected at E, corresponding to the mid-span locations of the two beams. Assume
both beams to have the same span L= 5m and the same flexural rigidity EI = 80000 kN-m2, and
torsional rigidity GJ = 0.2EI, with fixity (restraints against flexure and torsion) at both ends.
The beam AB is subject to a concentrated load of magnitude P=130kN, acting at the quarter-span
point F, as shown.
a) List the displacements and the member forces (7 marks)
b) Sketch the likely shapes (without values) of the shear force, bending moment and twisting moment
diagrams of AB and CD. (3 marks)
[Hint: Only 3 global coordinates are required!]
[You may make use of the grid element stiffness given below]
7. Figure 7 shows plane frame structure under lateral loading. Find the horizontal displacements at P, O
and N. Also find the maximum moment value and its location. Assume, E=200000000000 N/m2,
All vertical members have b = 0.4 m and d = 0.4 m;
All horizontal members have b = 0.3 m and d = 0.4 m; (10 marks)
Figure 6
Figure 7
Grid element and Transformation matrix
Grid element stiffness matrix
