CHENDU COLLEGE OF ENGINEERING &TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING

SUB CODE & SUB NAME : CE2351-STRUCTURAL ANALYSIS-II

UNIT-1 FLEXIBILITY METHOD FOR INDETERMINATE FRAMES

PART-A(2MARKS)

1. What is meant by indeterminate structures?

2. What are the conditions of equilibrium?Differentiate between determinate and indeterminate

structures.Determinate

3. Mention the mwthods available for the analysis of moving loads on beams.(NOV/DEC 2012)

4. Mention any two methods of determining the joint deflection of a perfect frame.(MAY/JUNE 2013)

5. Define degree of indeterminacy.

6. Explain indeterminacy of structures. (NOV/DEC 2013)

7. What are equilibirium equation. (NOV/DEC 2013)

8. Determine the degree of indeterminacy for the following 2D truss.

9. Determine the total, internal and external degree of indeterminacy for the plane rigid frame below.

10. Find the indeterminacy for the beams given below.

11. Find the indeterminacy for the given rigid plane frame.

12. Find the indeterminacy of the space rigid frame.

13. Differentiative pin jointed plane frame and rigid plane frame.(MAY/JUNE 2013)

14. Find the indeterminacy for the given space truss.

15. What are the different methods of analysis of indeterminate structures?

16. Briefly mention the two types of matrix methods of analysis of indeterminate structures.

17. Define kinematic indeterminacy (Dk) or Degree of Freedom (DOF) (MAY/JUNE 2013)

18. Briefly explain the two types of DOF.

19. Write The Condition For Maximum Reaction At One Support Of A Simply Supported Beam With A Moving

Single Point Load.(NOV/DEC 2012)

20. Define compatibility in force method of analysis .

21. Define the Force Transformation Matrix.

22. What are the requirements to be satisfied while analyzing a structure

23. Define flexibility influence coefficient (fij)

24. Write the element flexibility matrix (f) for a truss member & for a beam element.

25. Give the mathematical expression for the degree of static indeterminacy of rigid jointed plane frames. (NOV/DEC

2011)

26. What are the properties which characterize the structure response by means of force-displacement relationship?

(NOV/DEC 2011)

27. Write down the equation for the degree of static indeterminacy of the pin-jointed plane frames, explaining the

notations used. (MAY/JUNE 2012)

28. What are the conditions to be satisfied for determinate structures and how are indeterminate structures identified?

(MAY/JUNE 2012)

PART-B(16MARKS)

1.Analyze the pin-jointed plane frame shown in Figure Q. 11 (a) by flexibility matrix method. The flexibility for each

member.is 0.0025 mrn/kN. (MAY/JUNE 2012)

2.Analyze the continuous beam ABC shown in Figure by flexibility matrix method and draw the bending moment

diagram. (MAY/JUNE 2012)

3. Analyse the continuous beam show in Fig using force method. (APRIL/MAY 2011)

4. Analyse the portal frame ABCD shown in Fig .2 using force method (APRIL/MAY 2011)

5. Analyze the continuous beam ABC shown in Fig, by flexibility matrix method and sketch the bending moment

diagram. (NOV/DEC 2011)

6. Analyze the portal frame ABeD shown in Fig. by flexibility matrix method and sketch the bending moment

diagram.

(NOV/DEC

2011)

7.A Cantilever Of Length 15m Is Subjected To A Single Concentrated Load Of 15kn At The Middle Of The Span.

Find The Deflection At The Free End Usin Flexibility Matrix Method. Ei Is Uniform Throughout. (MAY/JUNE 2013)

8.A two span continous span from ABC is fixed at A and hinged at support B AND C. Span AB=BC=9m Set up

flexibility influence coefficient matrix assuming vertical reaction at B and C as redundants. .(MAY/JUNE 2013)

9.generate the flexibility matrix (α)for the structure with co-ordinate shown in fig.

2

3 1

4I,2A I,A

l/2 l/2

10.analyse the frame shown im fig. By the matrix flexibility method.

26kn/m 20kn

A B C

10m EI=3 EI=1 10m

11.analyse the frame shown im fig. By the matrix flexibility method.

16kn/m 16kn

A B C

10m EI=3 EI=1 10m

12.Using matrix flexibility method analyse the truss loaded as shown in fig and find the member forces A and E are

the same for all members. 16Kn

D 5m

A B C

3 m 3m

13.Develope the flexibility matrix for the structure with co ordinates shown in fig.

2 L 3

1 L EI= CONSTANT L

14. A two span continuous beam ABC is fixed at A and hinged at supports B and C. span of AB = span of BC = 13m.

set up flexibility influence co-efficient matrix assuming vertical reaction at B and C as redundant (NOV/DEC 2013)

15. Develope the flexibility matrix for the structure with co ordinates shown in fig

1 2 3 4

L L

16. Two wheel loads 90KN and 220 KN spaced 4m apart move on a girder of span 20 meters. Find the maximum

positive and negative shear force at a section 6 meters from the left end. Any whel load can load the other.

(NOV/DEC 2012)

UNIT-II MATRIX STIFFNESS METHOD

PART-A(2MARKS)

1. What are the basic unknowns in stiffness matrix method?

2. Define stiffness coefficient kij.

3. 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. What is the compatibility condition used in the flexibility method?

9. Write about the force displacement relationship.

10. Write the element stiffness for a truss element.

11. Write the element stiffness matrix for a beam ele ment.

12. Compare flexibility method and stiffness method.

13. Is it possible to develop the flexibility matrix for an unstable structure?

14. What is the relation between flexibility and stiffness matrix?

15. What are the types of structures that can be solved using stiffness matrix method?

16. Give the formula for the size of the Global stiffness matrix.

17. List the properties of the rotation matrix (MAY/JUNE 2013)

18. Why is the stiffness matrix method also called equilibrium method or displacement method?

19. what are influence lines (NOV/DEC 2012)

20. Write then stiffness matrix for a 2 D beam element.

21. What is degree of kinematic indetenninacy and give an example?(NOV/DEC 2011)

22. Write down the equation of element stiffness matrix as applied to 2D plane element. (NOV/DEC 2011)

23. Define degree of freedom of the structure with an example. (MAY/JUNE 2012)

24. Write a short note on global stiffness matrices. (MAY/JUNE 2012)

25. Define static indeterminacy. (APRIL/MAY 2011)

26. Define flexibility of a structure. (APRIL/MAY 2011)

27. . Write shorts notes element stiffness matrix.(MAY/JUNE 2013)

28. breifly explain muller breaslaus principle.(NOV/DEC 2012)

PART-B(16MARKS)

1. 1.Analyze the continuous beam ABC shown in Fig. by stiffness method and also draw the shear force diagram.

(MAY/JUNE 2012)

2. Analyze the portal frame ABeD shown in Fig. by stiffness method and also draw the bending moment diagram.

(MAY/JUNE 2012)

3. 3. Analyze the continuous beam ABC shown in Fig. by stiffness method and also sketch the bending moment

diagram. (NOV/DEC 2011)

4. 4. Analyze the fortal frame beam ABC shown in Fig. by stiffness method and also sketch the bending moment

diagram. (NOV/DEC 2011)

5. 5. Analyze the continuous beam ABC shown in Fig. by using displacement method and also sketch the bending

moment diagram. (APRIL/MAY 2011)

6. Analyze the truss shown in Fig. by using displacement method. (APRIL/MAY 2011)

7. A two span continous beam ABCD IS fixed at a simply supported over the supports B and C. AB=10m, BC=8m

moment of inertia is constant through out. A udl of 10 tons act an AB and udl 8 Ton/m act over BC. Analyse the

beam stiffness matrix method.

8.A portal frame ABCD with support A and D are fixed At same level UDL 8 Ton/m at span AB. SPAN

AB=BC=CD=9m. EI is constant throughout Analyse the frame by stiffness matrix method.

9. Analyse The Structure Shown In Fig By Stiffness Method

B W C

L L/2 L/2

A

10. Analyse the frame shown in fig by the matrix stiffness method.

A 60KN B 120KN C

2m 2m 4m 2m

11. Analyse the frame shown in fig by the matrix stiffness method.

A 30KN B 100KN C

2m 2m 4m 2m

12. A two span continous beam ABC is fixed at A and simply supported over the supports B& C. AB =6m, and

BC=6m The moment of inertia is constant throughout. A single udl 20kn/m at act on AB and point load 40kn/m act

an BC . Analyse the beam stiffness matrix method.

13. Develope the stiffness matrix for the structure with co ordinates shown in fig.

2 L 3

1 L EI= CONSTANT L

14.A two span continous beam ABCD IS fixed at a simply supported over the supports B and C. AB=8m, BC=6m

moment of inertia is constant through out. A UDL of 4 ton/m act an AB and single concentrated loadl 8 Ton act

over BC. Analyse the beam stiffness matrix method. (NOV/DEC 2013)

15. A portal frame ABCD with support A and D are fixed At same level UDL 8 Ton/m at span AB. SPAN

AB=BC=CD=9m. EI is constant throughout Analyse the frame by stiffness matrix method. (MAY/JUNE 2013)

16. A portal frame ABCD with supports A and D are fixed at a same level UDL 4 tons/m on the span BC. Span AB=

span BC= span CD=6m EI is constant is throughout. Analyse the frame by portal frame method. (NOV/DEC 2013)

17.A two span continuous beam abcd is fixed at A and simply supported over the supports B and C. span of AB= 10m

and BC= 8m. Moment of inertia is constant through out. A single concentrated load of 8 Ton/m acts over BC. Analyse

the beam by stiffness matrix method. (MAY/JUNE 2013)

UNIT III FINITE ELEMENT METHOD

PART-A(2MARKS)

1. What is meant by Finite element method?

2. List out the advantages of FEM.(APRIL/MAY 2011)

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 of structure?(MAY/JUNE 2013)

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?

19. What is meant by plane strain condition?

20. 20.What is the basic idea of mesh generation scheme? (NOV/DEC 2011)

21. State the stress-stain relationship in Cartesian co-ordinates. (NOV/DEC 2011)

22. What are the needs to satisfy the shape function? (MAY/JUNE 2012)

23. What is constant strain triangle? (MAY/JUNE 2012)

24.State any two types FEM. (APRIL/MAY 2011)

25.What Are The Triangular Elements (MAY/JUNE 2013)

26.define radial shear in arches.(NOV/DEC 2012)

27.write the importance of stiffening girders.

PART-B(16MARKS)

1.Develop the shape functions for an 8 noded brick element. (APRIL/MAY 2011)

2.Construct the shape functions of a 2D beam element. (APRIL/MAY 2011)

3. With a two dimensional triangular element model, derive for the displacement in the matrix form. (MAY/JUNE 2012)

4.For the two dimensional truss structure shown in Figure. formulate the global stiffness matrix [K]. The geometry

and loading aresymmetrical about centre line. Assume the area of cross section of all

members is the same. Take E = 2 X 108 kN / m2 (MAY/JUNE 2012)

5. Draw the typical finite elements. Explain with a triangular element model for displacement formulation. (NOV/DEC 2011)

6.Write a note on constant strain triangle. Explain in detail about the 4-nodded rectangular element to arrive the

stiffness matrix. (NOV/DEC 2011)

7.Briefly explain the truss element

8. Briefly explain the beam element.

9.Explain The Method Solving Plane Stress And Plane Strain Problems Using Finite Element Method. (MAY/2013)

10.Explain the types and applicatios of beam element in finite element method. (MAY/JUNE 2013)

11. E xplain the short notes on

What is meant by degrees of freedom?

What is truss element?

What is Rayleigh-Ritz method?

What is Aspect ratio?

What are the h and p versions of finite element method?

12. Using Rayleigh Ritz methods calculate the deflection at the middle and end for the following cantilever beam.

13. For a tapered plate of uniform thickness t=10mm, find the displacement at the nodes by forming into two element

model. The bar has mass density ρ=7800 kg/m3, Youngs modulus, E=2*10^5MN/m2.In addition to self-weight, the

plate is subjected to the point load p=10kN at its centre.

14. For the two bar truss shown in fig determine the displacement of node 1 & stress in element 1-3.

15. Determine the stiffness matrix for the CST shown infig. Assume plane stress conditions. Co ordinates are in mm.

Take E = 210 GPa , υ= 0.25, t= 10 mm

16. Explain the following (i) constant strain angle (ii) linear strain triangle (NOV/DEC 2013)

17. Explain the types and applicatios of beam element in finite element method. (NOV/DEC 2013)

UNIT – IV PLASTIC ANALYSIS OF STRUCTURES

PART-A(2MARKS)

1. What is a plastic hinge?. (MAY/JUNE 2012)

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.

8. Mention the section having maximum shape factor.

9. Define load factor and collapse load (NO/DEC 2011)

10. State upper bound theory. (MAY /JUNE 2013)

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 a ordinary circular

18. section?

19. explain pure bending. (NOV /DEC 2013)

20. Give the theorems for determining the collapse load.

21. Define plastic modulus and shape factor.

22. What are meant by load factor and collapse load?

23. Define plastic hinge with an example. (MAY /JUNE 2013)

24. What is collapse load and define load factor? (MAY/JUNE 2012)

25. What is shape factor (NOV/DEC 2011)

26. .DEFINE PLASTIC MODULUS (NOV/DEC 2011)

PART-B(16MARKS)

1. Determine the plastic moment capacity of the beam shown in Fig 2

2.Determine the minimum plastic moment capacity of the frame to prevent collapse

3.Determine the shape factor of a T-section beam of flange dimension 100x12 mm and web dimension 138 x 12 mm

thick. (MAY/JUNE 2012)

4.Determine the collapse load 'W', for a three span continues beam of constant plastic moment 'Mp', loaded as shown

in Fig.(MAY/JUNE 2012)

5.A simply supported beam of span 5m is to be designed for a UDL of 25 kN m. Design a suitable I section using

plastic theory, assuming yield stress in steel as fy = 250 N/mm2. (NOV/DEC 2011)

6. Analyze a propped cantilever of length 'L and subjected to UDL of w/m length for the entire span and find the

collapse load. (NOV/DEC 2011)

7.A beam of span 6m is to be designed for an ultimate udl of 25 kn/m. the beam is simply supported at the ends design

a suitable I section using plastic theory, assuming σy=250n/mm2.

8. A two span continous beam ABC is fixed at A and simply supported over the supports B& C. AB =6m, and

BC=6m The moment of inertia is constant throughout. A single udl 20kn/m at act on AB and point load 40kn/m act

an BC . if the load factor is 1.80 and the slope factor is 1.15 for the I section find the section modulus needed. Assume

yield stress for the material as 250kn/m2.

9. A two span continous beam ABC has span length AB =6m, and DC=6m AND CARRIES A udl of 30 kn/m

completely covering the spans AB and BC. A and C are simple supports if the load factor is 1.80 and the slope factor

is 1.15 for the I section find the section modulus needed. Assume yield stress for the material as 250kn/m2.

10.find the collapse load for the frame shown in fig.

W

l/2 l/2

MP

l/2

w/2

2MP 2MP

l/2

11. 10.find the collapse load for the frame shown in fig.

W

2m 2m

w B E C

3m

4m

A

D

12. A Uniform beam of span 3m and fully plastic moment Mpis simply supported at one end and rigidly clamped at

other end. A concentrated load of 10 KN may be applied anywhere within the span. Find the smallest value of Mp

such that collapse would first occur when the load is in its most unfavourable position. (NOV/DEC 2012)

13. A continous beam ABC is loaded as shown in fig.determine required MP if the load factor is 3.2

5kn/m 60kn 90kn

A B C

MP 2MP

12m 8m 8m 8m

14. A simply supported beam of span 8m is to be designed for a UDL of 50 kN m. Design a suitable I section using

plastic theory, assuming yield stress in steel as fy = 150 N/mm2.

15. A Rectangular portal frame of span L and height L/2 is fixed to the ground at both ends has a uniform section

section throughout with its fully plastic moment of resistance equal to My. It is loaded with a point load w at centre of

sapn as well as a horizontal force W/2 at its top right corner. Calculate the value of W at collapse of the

frame.(NOV/DEC 2012)

16. Derive the shape factor for I- section and circular section. (APRIL/MAY 2011)

17. Find the fully plastic moment required for the frame shown in Fig.5 if all the members have same value of Mp.

(APRIL/MAY 2011)

18. Explain the following (NOV/DEC 2013)

Plastic modulus

Shape factor

Load factor

19. A uniform beam of span 5m and fully plastic moment Mp is simply supported is one end and rigidly clamped at

other end. A concentrated load of 20KN may be applied anywhere within the span.Find thr smallest value of Mp.

Such that collapse would first occur when the load is in its most unfavourable position. (NOV/DEC 2013

UNIT-V CABLE AND SPACE STRUCTURES

PART-A(2MARKS)

1. What are cable structures?

2. What is the true shape of cable structures?

3. What is the nature of force in the cables?

4. Differentiative curved beams and beam curved plan. (NOV/DEC 2013)

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?

10. Differentiate between plane truss and space truss.

11. Define tension coefficient of a truss member.

12. Give some examples of beams curved in plan. (APRIL/MAY 2011)

13. What are the forces developed in beams curved in plan?

14. What are the significant features of circular beams on equally spaced supports?

15. Give the expression for calculating equivalent UDL on a girder.

16. Give the range of central dip of a cable.

17. Give the application of three hinged stiffening girder. (NOV/DEC 2013)

18. Give the types of significant cable structures

19. Write stresses in suspended wires due to self weight. (APRIL/MAY 2011)

20. Define tension coefficient For what type of structures tension coefficient method is employed? (NOV/DEC 2011)

21. What are the components of forces acting on the beams curved in plan and show the sign conventions of these

forces? (NOV/DEC 2011)

23. Define a space frame and what is the nature of joint provided in the space trusses? (MAY/JUNE 2012)

24. What are the types of stiffening girders? (MAY/JUNE 2012)

25.What is the need of cable structures. (MAY/JUNE 2013)

26. What are the methods available for the analysis of space trusses. (MAY/JUNE 2013)

27.The two hinged stiffening girder has one degree of indeterminacy.

PART-B(16MARKS)

1. A three hindged stiffening girder of a suspension bridge of 100 m span subjected to two point loads 10 kN each

placed at 20 m and 40 m, respectively from the left hand hinge. Determine the bending moment and shear force in the

girder at section 30 m from each end. Also determine the maximum tension in the cable which has a central dip of

10m.

2. A suspension bridge has a span 50 m with a 15 m wide runway. It is subjected to a load of 30 kN/m including self

weight. The bridge is supported by a pair of cables having a central dip of 4m. Find the cross sectional area of the

cable necessary if the maximum permissible stress in the cable material is not to exceed 600 MPa. (NOV/DEC 2011)

3. A quarter circular beam of radius 'R' curved in plan is fixed at A and free at B as shown in

It carries a vertical load-P at its free end. Determine the deflection at free end and draw the bending moment and

torsional moment diagrams. Assume flexural rigidity (El) = torsional rigidity (GJ). (MAY/JUNE 2012)

4. A three hindged stiffening girder of a suspension bridge of 100 m span subjected to two point loads 10 kN each

placed at 20 m and 40 m, respectively from the left hand hinge. Determine the bending moment and shear force in the

girder at section 30 m from each end. Also determine the maximum tension in the cable which has a central dip of

10m. (MAY/JUNE 2012)

5. A suspension cable is supported at two point "A" and "B" , "A" being one metre above "B". The distance AB being

20m. The cable is subjected to 4 loads of 2kN, 4kN, 5kN and 3kN at distances of 4m, 8m, 12m and 16m ,respectively

from "A". Find the maximum tension in the cable, if the dip of the cable at point of application of first load is 1m with

respect to level at A. Find. also the length of the cable. (APRIL/MAY 2011)

6. Derive the expressions for BM, SF and TM in a semicircular beam simply support-ted oni,'three supports equally

spaced. (APRIL/MAY 2011)

7.A suspension cable bridge of 100mm span has two three hinged stiffening girders supported girders supported by

twocables with a central dip of 10m. I f three point loads of 20kn each are placed along the centre line of the roadway

at 10,15 and 20m from left hand hinge find the shear force and bending moment in each girders at 30m from each

end.calculate the maximum tension in the cable.

8. A suspension cable of 75m horizontal span and central dip 6m has a stiffening girders 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 udl

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.

9. A suspension cable bridge of 80m and central dip 8m is subjected from the same level at two towers. T he bridge

cable is stiffened by a three hinged stiffening girder which carries a single concentrated load of 20 KN at a point of

30m from one end. S ketch the SFD for the girder. (MAY/JUNE 2013)

10.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. I tis fixed at A and free at B as shown in fig. IT carries a vertical concentrated load W at the free end

B. compute the sf, bm and twisting moment value and sketch variations of the above quantities. A lso determine the

vertical deflection of the free and B.

11. A suspension bridge cable of of 90 m and central dip is suspende by the same level at two towers. The bridge

cable is stiffened by the three hinged stiffening girder which carries a single concentrated load of 25KN at a point of

40m from one end. Sketch the SFD for the girder. (NOV/DEC 2013)

12.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 a udl of w/unit run over the entire length of the beam. Calculated the

sketck the variations of same also determine the deflection at the free end B.

13. A Suspension bridge cable of span 75m and central dip 7m is suspended from the same level at two towers. The

bridge cable is stiffened by a three hinged stiffening girder which carries a single concentrated load of 15 KN at a

point of 25m from one end. Sketch the SFD for the girder. (NOV/DEC 2012)

14. Derive the expression for bending moment and torsIon for a semi circular beam of radius R. The cross section of

the material is circular with radius R. It is loaded with a load at the mid point of the semicircle. (MAY/JUNE 2013)

15.U sing the method of tension coefficient analyse the cantilever plane truss shown in fig. and find the member

forces.

40kn 4kn

2m B 2m c

3m A

D