CE2351-STRUCTURAL ANALYSIS II

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1 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.

2 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 (f ij ). 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.

3 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.

4 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.

5 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.

6 10. Analyse the portal frame shown in figure using matrix flexibility method.

7 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?

8 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.

9 4. Analyse the structure shown in figure by stiffness method. 5. Analyse the frame shown in figure by the matrix stiffness method.

10 6. Analyse the frame shown in figure by stiffness method. 7. Analyse the frame shown in figure by the matrix stiffness method.

11 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 BD CD

12 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 BD

13 10. Analyse the portal frame with fixed base shown in the figure using the matrix stiffness method,given I AB =3I₀;I BC =2I₀;I CD =3I₀.

14 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?

15 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 =[ ] {P₂} T =[ ]

16 {P₃} T =[ ] 10.Solve the matrix equation {f}=[k]{u} where {f} T =[100, 120, -10]and [K] is { }

17 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

18 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 σ y =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 M p if the load factor is3.2.

19 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,m p is the same for all members.

20 9.Find the collapse load for the portal frame loaded as shown.

21 10 Find the collapse load for the loaded frame loaded as shown.

22 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?

23 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.

24 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.

25 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.

26 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

27 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.

CE2302 STRUCTURAL ANALYSIS I Important Questions PART B

CE2302 STRUCTURAL ANALYSIS I Important Questions PART B UNIT I 1. Determine the vertical and horizontal displacement of the joint B in a pin jointed frame shown in fig. 2. The cross sectional area of each