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CE2351-STRUCTURAL ANALYSIS II
QUESTION BANK
UNIT-I
FLEXIBILITY METHOD
PART-A
1. What are determinate structures? 2. What is meant by
indeterminate structures? 3. What are the conditions of
equilibrium? 4. Differentiate between determinate and indeterminate
structures. 5. What do you mean by redundancy? 6. Differentiate
between pin jointed and rigid jointed plane frames 7. What are
compatibility conditions? 8. Define degree of indeterminacy. 9.
Define internal and external indeterminacies. 10. Find the
indeterminacy for the beams given below.
11. Find the indeterminacy for the given rigid plane frame.
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12. What are the different methods of analysis of indeterminate
structures? 13. Briefly mention the two types of matrix methods of
analysis of indeterminate structures. 14. Define a primary
structure. 15. Define kinematic indeterminacy or Degree of Freedom
(DOF) 16. Briefly explain the two types of DOF. 17. Define
compatibility in force method of analysis. 18. Define the Force
Transformation Matrix. 19. What are the requirements to be
satisfied while analyzing a structure? 20. Define flexibility
influence coefficient (fij). 21. Write the element flexibility
matrix (f) for a truss member & for a beam element.
PART-B
1. Analysethe continuous beam shown in figure by the flexibility
method and draw the
bending moment diagram.
2. Analysethe continuous beam shown in figure by the flexibility
method and draw the
bending moment diagram.
3. Analyse the frame shown in the figure by the matrix
flexibility method.
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4. A statically indeterminate frame shown in the figure carries
a load of 80 kN,Analyse the
frame by matrix flexibility method. A and E are same for all
members.
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5. Analyse the truss loaded as shown in the figure using matrix
flexibility method and find
the member forces.A and E are the same for all members.
6. Analysethe continuous beam shown in figure using the matrix
flexibility method.
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7. Analysethe continuous beam shown in figure .Assume EI as
uniform.Use Matrix
flexibility method.
8. Using matrix flexibility method,analyse the continuous beam
loaded as shown in the
figure.
9. Analyse the rigid jointed portal frame shown in the figure by
the matrix flexibility
method.
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10. Analyse the portal frame shown in figure using matrix
flexibility method.
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UNIT-II
STIFFNESS MATRIX METHOD
PART-A
1. What are the basic unknowns in stiffness matrix method? 2.
Define stiffness coefficient. 3. What is the basic aim of the
stiffness method? 4. What is the displacement transformation
matrix? 5. How are the basic equations of stiffness matrix
obtained? 6. What is the equilibrium condition used in the
stiffness method? 7. What is meant by generalized coordinates? 8.
Write about the force displacement relationship. 9. Write the
element stiffness matrix for a truss element. 10. Write the element
stiffness matrix for a beam element. 11. Compare flexibility method
and stiffness method. 12. Is it possible to develop the flexibility
matrix for an unstable structure? 13. What is the relation between
flexibility and stiffness matrix? 14. What are the types of
structures that can be solved using stiffness matrix method? 15.
Give the formula for the size of the Global stiffness matrix. 16.
List the properties of the rotation matrix. 17. Why the stiffness
matrix method also called equilibrium method or displacement
method?
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18. Write then stiffness matrix for a 2 D beam element. 19.
Define displacement vector. 20. Write a note on global stiffness
matrix. 21. Define load vector.
PART-B
1. Analyse the continuous beam shown in figure by stiffness
method.Draw the bending
moment diagram.
2. A two span continuous beam ABC is fixed at A and simply
supported over the supports B
and C. AB=6m and BC=6m.The moments of inertia is constant
throughout.It is loaded as
shown in the diagram.Analyse the beam by matrix stiffness
method.
3. Analysethe continuous beam by matrix stiffness method .
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4. Analyse the structure shown in figure by stiffness
method.
5. Analyse the frame shown in figure by the matrix stiffness
method .
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6. Analyse the frame shown in figure by stiffness method .
7. Analyse the frame shown in figure by the matrix stiffness
method .
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8. Usingmatrix stiffness method ,analyse the truss for the
member forces in the truss loaded
as shown. AE and Lare tabulated below for all the three
members.
Member AE(MN) L(cm)
AD 400 400
BD 461.9 461.9
CD 800 800
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9. Find the bar forces in thetruss shown in figure by stiffness
method. AE and L for all
members are tabulated below.
Member AE L
(MN) (cm)
AD,CD 300 300
BD 259.8 259.8
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10. Analyse the portal frame with fixed base shown in the figure
using the matrix stiffness
method ,given
IAB=3I₀;IBC=2I₀;ICD=3I₀.
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UNIT-III
FINITE ELEMENT METHOD
PART-A
1. What is meant by Finite element method? 2. List out the
advantages of FEM. 3. List out the disadvantages of FEM. 4. Mention
the various coordinates in FEM. 5. What are the basic steps in FEM?
6. What is meant by discretization? 7. What are the factors
governing the selection of finite elements? 8. Define displacement
function. 9. Briefly explain a few terminology used in FEM. 10.
What are different types of elements used in FEM? 11. What are 1-D
elements? Give examples. 12. What are 2-D elements? Give examples.
13. What are 3-D elements? Give examples. 14. Define Shape
function. 15. What are the properties of shape functions? 16.
Define aspect ratio. 17. What are possible locations for nodes? 18.
What are the characteristics of displacement functions?
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19. What is meant by plane stress condition? 20. Define beam
element. 21. Define triangular elements.
PART-B
1.Explain the procedure of adopting finite element method.
2.Explain the discretisation process in detail.
3.Compute the nodal loads on each of the 3 elements for a fixed
beam AB of span L with a point
load W & 2W located at one third span from end A & B
respectively .
4.Determine the element load vectors and global load vector for
the system in the figure-A.
5.For the beam shown in figure-A, determine the{P} vectors and
the {F} vector by equivalent
load method.
Fig - A
6.Explain the procedure for assembling of force vectors and
stiffness matrices.
7. Explain the procedure for formulating the stiffness matrix
for a constant strain element.
8. Explain the formulation of Pascal Triangle.
9.Assemble the elements 1,2 and 3 in the figure to develop the
global load vectors and the global
stiffness matrix,given that
{P₁}T=[8 0 6 0 2 0]
{P₂}T=[5 1 3 0 6 0 9 2]
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{P₃}T=[0 2 0 2]
10.Solve the matrix equation {f}=[K]{u} where {f}T=[100, 120,
-10]and [K] is
12 6 2
{ 6 48 4 }
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2 4 24
Make sure that u₁=0.
UNIT-IV
PLASTIC ANALYSIS OF STRUCTURES
PART-A
1. What is a plastic hinge? 2. What is a mechanism? 3. What is
difference between plastic hinge and mechanical hinge? 4. Define
collapse load. 5. List out the assumptions made for plastic
analysis. 6. Define shape factor. 7. List out the shape factors for
the following sections.
a) Rectangular section, b) Triangular section, c) Circular
section, d) Diamond section
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8. Mention the section having maximum shape factor. 9. Define
load factor. 10. State upper bound theory. 11. State lower bound
theory. 12. What are the different types of mechanisms? 13. Mention
the types of frames. 14. What are symmetric frames and how they
analyzed? 15. What are unsymmetrical frames and how are they
analyzed? 16. Define plastic modulus of a section Zp. 17. How is
the shape factor of a hollow circular section related to the shape
factor of an
ordinary circular section?
18. Give the governing equation for bending. 19. Give the
theorems for determining the collapse load. 20. State plastic
moment of resistance. 21. Explain pure bending with its
assumptions.
PART-B
1.Calculate the shape factor for a a)rectangle section of
breadth’b’ and depth ‘d’, b)diamond
section of breadth’b’ and depth’d’.
2.Calculate the shape factor for a triangle a)centroid lying at
d/3 from the base of
depth’d’,andbreadth’b’. b)circular section of dia ‘D’.
3.A mild steel I-section 200mm wide and 250mm deep has a mean
flange thickness of 20mm
and a web thickness of 10mm.Calculate the S.F.Find the fully
plastic moment if σy=252N/mm².
4.Find the shape factor of the I-section with top flange 100mm
wide,bottom flange 150mm
wide,20mm tk and web depth 150mm and web thickness 20mm.
5.Find the shape factor of the T-section of depth 100mm and
width of flange
100mm,flangethickness and webthickness 10mm.
6.Acontinuous beam ABC is loaded as shown .Determine the
required Mp if the load factor is3.2.
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7. A two span continuous beam ABC has span length AB=6m and
BC=6m and carries an udl of
30 kN/m completely covering the spans AB and BC.A and C are
simple supports.If the load
factor is 1.8 and the shape factor is 1.15 for the I-section
,find the section modulus,assume yield
stress for the material as 250N/mm².
8.Determinethe collapse load for the frame shown in the
diagram,Mp is the same for all
members.
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9.Find the collapse load for the portal frame loaded as
shown.
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10 Find the collapse load for the loaded frame loaded as
shown.
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UNIT-V
CABLE AND SPACE STRUCTURES
PART-A
1. What are cable structures? Mention its needs. 2. What is the
true shape of cable structures? 3. What is the nature of force in
the cables? 4. What is a catenary? 5. Mention the different types
of cable structures. 6. Briefly explain cable over a guide pulley.
7. Briefly explain cable over saddle. 8. What are the main
functions of stiffening girders in suspension bridges? 9. What is
the degree of indeterminacy of a suspension bridge with two hinged
stiffening
girder?
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10. Differentiate curved beams and beams curved in plan. 11.
Differentiate between plane truss and space truss. 12. Define
tension coefficient of a truss member. 13. What are curved beams?
14. What are the forces developed in beams curved in plan? 15. What
are the significant features of circular beams on equally spaced
supports? 16. Give the expression for calculating equivalent UDL on
a girder. 17. Give the range of central dip of a cable. 18. Give
the expression for determining the tension in the cable. 19. Give
the types of significant cable structures 20. Give examples of
three hinged stiffened girder. 21. What are the methods available
for the analysis of space truss?
PART-B
1. Using the method of tension coefficients,analyse the space
truss shown in the figure and
find the forces in the members of the truss.
2. Analyse the space truss shown in the figure by the method of
tension coefficients and
determine the member forces.
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3. A curved beam in the form of a quadrant of a circle of radius
R and having a uniform
cross section is in a horizontal plane.It is fixed at A and free
at B as shown in the figure.
It carries a vertical concentrated load W at the free end
B.Computethe shear
force,bending moment and twisting moment values and sketch
variations of the above
quantities.Also determine the vertical deflection of the free
end B.
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4. A curved beam AB of uniform cross section is horizontal in
plan and in the form of a
quadrant of a circle of radius R .The beam is fixed at A and
free at B.It carries
auniformly distributed load of w/unit run over the entire length
of the beam as
shown.Calculate the shear forces,bending moment and Twisting
moment value,atAand B
and sketch the variations of the same.Also determine the
deflection at the free end B.
5. Diagram shows a curved beam,semi-circular in plan and
supported on three
equallyspaced supports.The beam carries a uniformly distributed
load of w/unit of the
circular length.Analyse the beam and sketch the bending moment
and twisting moment
diagrams.
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6. A suspension cable having supports at the same level,has a
span of 30m and a maximum
dip of 3m.The cable is loaded with a udl of 10kN/m throughout
its length.Find the
maximum tension in the cable.
7.A suspension bridge of 250m span has two nos of three hinged
stiffening girdness supported by
cables with a central dip of 25m.If 4 point load of 300kN each
are placed at the centre line of the
roadway at 20,30,40 and 50m from the left hand hinge, find the
shear force and bending moment
in each girder at 62.5m from each end.Calculate also the maximum
tension in the cable.
8.A suspension cable is supported at 2 points 25m apart .The
left support is 2.5m above the right
support.The cable is loaded with a uniformly distributed load of
10kN/m throughout the
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span.The maximum dip in the cable from the left support is
4m.Find the maximum and minimum
tensions in the cable.
9.A suspension cable of 75m horizontal span and central dip 6m
has a stiffening girder hinged at
both ends. The dead load transmitted to the cable including its
own weight is 1500kN.The girder
carries a live load of 30kN/m uniformly distributed over the
left half of the span.Assuming the
girder to be rigid,calculate the shear force and bending moment
in the girder at 20m from the left
support.Also calculate the maximum tension in the cable.
10.A suspensioncable has a span of 120m and a central dip of10m
is suspended from the same
level at both towers.The bridge is stiffened by a stiffening
girder hinged at the end supports.The
girder carries a single concentrated load of 100kN at a point
30m from left end.Assuming equal
tension in the suspension hangers. Calculate
i)the horizontal tension in the cable
ii)the maximum positive bending moment.
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