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# Structeral Analysis

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DEPARTMENT OF CIVIL ENGINEERING ANNA UNIVERSITY QUESTION BANK CE 2302 – STRUCTURAL ANALYSIS-I TWO – MARK QUESTIONS DEFLECTION OF DETERMINATE STRUCTURES UNIT I 1. 2. 3. 4. 5. 6. 7. Write any two important assumptions made in the analysis of trusses? Differentiate perfect and imperfect trusses? Write the difference between deficient and redundant frames? What are the situations wherein sway will occur in portal frames? Define degrees of freedom. State Castiglione’s first theorem? Define Flexural Rigidity of Beams MOVING LOADS AND INFLUENCE LINES

UNIT II 8. What is meant by ILD? 9.

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What are the uses of influence line diagrams? 10. State Muller Breslau’s principle. 11. Sketch the influence line diagram for shear force at any section of a simply supported beam 12. In the context of rolling loads, what do you understand by the term equivalent uniformly distributed load? 13. How will you obtain degree of static determinacy? 14. What is degree of kinematic indeterminacy UNIT III ARCHES 15. State the types of arches. 16. What is a three hinged arch? 17. Write the equation to define the centre line of a circular arch? 18.

Name the different types of arch as per structure configuration 19. Give an expression for the determination of horizontal thrust of a two hinged arch considering bending deformation only 20. Explain the transfer of load to the arches. 21. Differentiate between the cable and arch. 22. Write down the expression for the horizontal thrust when the two hinged arch is subjected to uniformly distributed load thought the span. 23. What the degree of redundancy of two hinged arch? 24. Explain the term Horizontal thrust. www. Vidyarthiplus. com Page 1 www. Vidyarthiplus. com 25.

What is ‘H’ of the symmetrical two hinged parabolic arch due to UDL extending to the full length of span? Take central rise = span. 26. A symmetrical three hinged arch (circular) supports a load ‘W’ at the crown. What is the 1 8 value of H? 27. What is the degree of static indeterminacy of a three hinged parabolic arch? UNIT-IV SLOPE DEFLECTION METHOD 28. State relative merit of moment distribution method over slope deflection method. 29. Name the three classical force methods used in the analysis of continuous beams. 30. What are the limitations of slope deflection method? 1. Draw the deflected shape of the beam shown 32. Write down the equilibrium equations used in slope deflection methods. 33. Why is slope deflection equation method known as stiffness method? 34. What are the basic assumptions made in slope deflection method? UNIT-V MOMENT DISTRIBUTION METHOD 35. What are the advantages of slope-deflection method over moment distribution method? 36. What is meant by relative stiffness of a member? 37. Define carry over factor? 38. Define distribution factor and carry over factor in moment distribution method. 39. 40. 41. 42. 43. 44.

Explain the terms ‘distribution factor’ and ‘carry over factor’ State stiffness of a member. Define distribution factor. What is relative stiffness? Write the three moment equation for general case. Determine the fixed end moment of the beam shown in fig. 45. Define Stiffness factor. 46. What do you mean by carry over factor? www. Vidyarthiplus. com Page 2 www. Vidyarthiplus. com 47. Write the expression for fixed end moment for a beam subjected to sinking of support by an amount?. 48. Give the carry over factor of a bending member when the far end is (i) hinged (ii) fixed. 49.

State the advantages of continuous beam over simply supported beam. PART –B QUESTION UNIT –II 1. A beam ABC is supported at A, B and C as shown in Fig. 7. It has the hinge at D. Draw the influence lines for (1) reactions at A, B and C (2) shear to the right of B (3) bending moment at E A D B E C 2m 4m 3m 8m 2. Determine the influence line ordinates at any section X on BC of the continuous beam ABC shown in Fig. 8, for reaction at A. X A B x C 5m 5m 3. In Fig. 1, D is the mid point of AB. If a point load W travels from A to C along the span where and what will be the maximum negative bending moment in AC. A

D B C l www. Vidyarthiplus. com l/3 Page 3 www. Vidyarthiplus. com Fig. 1 2. 3. 4. In Fig. 1 above, find the position and value of maximum negative shear. For the beam in Fig. 1, sketch the influence line for reaction at B and mark the ordinates. Sketch qualitatively the influence line for shear at D for the beam in Fig. 2. (Your sketch shall clearly distinguish between straight lines and curved lines) A B D 0. 8 l l 1. 6 l C 5. A single rolling load of 100 kN moves on a girder of span 20m. (a) Construct the influence lines for (i) Shear force and (ii) Bending moment for a section 5m from the left support. b) Construct the influence lines for points at which the maximum shears and maximum bending moment develop. Determine these maximum values. 6. Derive the influence diagram for reactions and bending moment at any section of a simply supported beam. Using the ILD, determine the support reactions and find bending moment at 2m, 4m and 6m for a simply supported beam of span 8m subjected to three point loads of 10kN, 15kN and 5kN placed at 1m, 4. 5m and 6. 5m respectively. 7. Two concentrated rolling loads of 12 kN and 6 kN placed 4. 5 m apart, travel along a freely supported girder of 16m span.

Draw the diagrams for maximum positive shear force, maximum negative shear force and maximum bending moment. (or) 12. Determine the influence line for RA for the continuous beam shown in the fig. 1. Compute influence line ordinates at 1m intervals. www. Vidyarthiplus. com Page 4 www. Vidyarthiplus. com Analyse the continuous beam shown in figure by slope deflection method and draw BMD. EI is constant. UNIT-III ARCHES 1. A three hinged parabolic arch of span 100m and rise 20m carries a uniformly distributed load of 2KN/m length on the right half as shown in the figure. Determine the maximum bending moment in the arch. . A two hinged parabolic arch of span 20m and rise 4m carries a uniformly distributed load of 5t/m on the left half of span as shown in figure. The moment of inertia I of the arch section at any section at any point is given by I = I0 sec ? where ? = inclination of the tangent at the point with the horizontal and I0 is the moment of inertia at the crown. Find (a) (b) (c) the reactions at the supports the position and the value of the maximum bending moment in the arch. 3. A three hinged symmetric parabolic arch hinged at the crown and springing, has a span of 15m with a central rise of 3m.

It carries a distributed load which varies uniformly form www. Vidyarthiplus. com Page 5 www. Vidyarthiplus. com 32kN/m (horizontal span) over the left hand half of the span. Calculate the normal thrust; shear force and bending moment at 5 meters from the left end hinge. 4. A two hinged parabolic arch of span 30m and central rise 5m carries a uniformly distributed load of 20kN/m over the left half of the span. Determine the position and value of maximum bending moment. Also find the normal thrust and radial shear force at the section.

Assume that the moment of inertia at a section varies as secant of the inclination at the section. 5. A three hinged parabolic arch, hinged at the crown and springing has a horizontal of 15m with a central rise of 3m. If carries a udl of 40kN/m over the left hand of the span. Calculate normal thrust, radial shear and bending moment at 5m from the left hand hinge. 6. A parabolic two hinged arch has a span L and central rise ‘r’. Calculate the horizontal thrust at the hinges due to UDL ‘w’ over the whole span. 7. Derive an expression for the horizontal thrust of a two hinged parabolic arch. Assume, I = Io Sec?. 8.

A three hinged parabolic arch of span 20 m and rise 4m carries a UDL of 20 kN/m over the left half of the span. Draw the BMD. 9. A parabolic 3 hinged arch shown in fig. 9 carries loads as indicated. Determine (i) resultant reactions at the 2 supports (ii) bending moment, shear (radial) and normal thrust at D, 5m from A. (7) (3+3+3) 30 kN 3m 20 kN D 5m 5m A 4m 3m C 25 kN/m B 20m www. Vidyarthiplus. com Page 6 www. Vidyarthiplus. com ° ° 10. A symmetrical parabolic arch spans 40m and central rise 10m is hinged to the abutments and the crown. It carries a linearly varying load of 300 N/M at each of the abutments to zero at the crown.

Calculate the horizontal and vertical reactions at the abutments and the position and magnitude of maximum bending moment. 11. A three hinged stiffening girder of a suspension bridge of span 100m is subjected to two points loads of 200 kN and 300 kN at a distance of 25 m and 50 m from the left end. Find the shear force and bending moment for the girder. 12. In a simply supported girder AB of span 20m, determine the maximum bending moment and maximum shear force at a section 5m from A, due to passage of a uniformly distributed load of intensity 20 kN/m, longer than the span. 3. The figure shows a three hinged arch with hinges at a A, B and C. The distributed load of 2000N/m acts on CE and a concentrated load of 4000N at D. Calculate the horizontal thrust and plot BMD. UNIT-IV SLOPE DEFLECTION METHOD Page 7 www. Vidyarthiplus. com www. Vidyarthiplus. com 1. Analyse the continuous beam given in figure by slope deflection method and draw the B. M. D (or) 2. Analyse the frame given in figure by slope deflection method and draw the B. M. D 3. Analyse the continuous beam given in figure by slope deflection method and draw the B. M. D (or) 4.

Analyse the frame given in figure by slope deflection method and draw the B. M. D. www. Vidyarthiplus. com Page 8 www. Vidyarthiplus. com 5. Analyse the continuous beam given in figure by slope deflection method and draw the B. M. D 6. Using slope deflection method, determine slope at B and C for the beam shown in figure below. EI is constant. Draw free body diagram of BC. (or) 7. Analysis the frame shown in below by the slope deflection method and draw the bending moment diagram. Use slope deflection method. www. Vidyarthiplus. com Page 9 www. Vidyarthiplus. com 8.

A continuous beam ABCD consist of three span and loaded as shown in fig. 1 end A and D are fixed using slope deflection method Determine the bending moments at the supports and plot the bending moment diagram. (or) 9.. A portal frame ABCD, fixed at ends A and D carriers a point load 2. 5Kn as shown in figure – 2. Analyze the portal by slope deflection method and draw the BMD. www. Vidyarthiplus. com Page 10 www. Vidyarthiplus. com 10. Using slope deflection method analyse the portal frame loaded as shown in Fig (1). EI is constant. (or) 11. Using slope deflection method analyse a continuous beam ABC loaded as shown in Fig (2).

The ends A and C are hinged supports and B is a continuous support. The beam has constant flexural rigidity for both the span AB and BC. UNIT –V MOMENT DISTRIBUTION METHOD 1. Draw the bending moment diagram and shear force diagram for the continuous beam shown in figure below using moment distribution method. EI is constant. www. Vidyarthiplus. com Page 11 www. Vidyarthiplus. com (or) 2. Analysis the frame shown in figure below for a rotational yield of 0. 002 radians anticlockwise and vertical yield of 5mm downwards at A. assume EI=30000 kNm2. IAB = ICD = I; IBC = 1. 51.

Draw bending moment diagram. Use moment Distribution Method. 3. Draw the bending moment diagram and shear force diagram for the continuous beam shown in figure below using moment distribution method. EI is constant. . (or) 4. Draw the bending moment diagram and shear force diagram for the continuous beam shown in figure below using moment distribution method. EI is constant. . www. Vidyarthiplus. com Page 12 www. Vidyarthiplus. com 5. A continuous beam ABCD if fixed at A and simply supported at D and is loaded as shown in figure 3. spans AB, BC and CD have MI of I,I-SI, and I respectively.

Using moment distribution method determine the moment at the supports and draw the BMD. (or) 6. Analyse and draw the BMD for the frame shown in figure 4. using moment the frame has stiff joint at B and fixed at A,C and D. www. Vidyarthiplus. com Page 13 www. Vidyarthiplus. com 7. A beam ABCD, 16m long is continuous over three spans AB=6m, BC = 5m & CD = 5m the supports being at the same level. There is a udl of 15kN/m over BC. On AB, is a point load of 80kN at 2m from A and CD there is a point load of 50 kN at 3m from D, calculate the moments by using moment distribution method. Assume EI const. (or) 8.

A continuous beam ABCD 20m long carried loads as shown in figure 5. Find the bending moment at the supports using moment distribution method. Assume EI const. 9. Analyse a continuous beam shown in Fig (3) by Moment distribution method. Draw BMD. www. Vidyarthiplus. com Page 14 www. Vidyarthiplus. com (or) 10. Using Moment Distribution method, determine the end moments of the members of the frame shown in Fig (4) EI is same for all the members. 11. A continuous beam ABCD of uniform cross section is loaded as shown in Fig(5) Find (a) Bending moments at the supports B and C (b) Reactions at the supports.

Draw SFD and BMD also 12. A two span continuous beam fixed at the ends is loaded as shown in Fig(6). Find (a) Moments at the supports. www. Vidyarthiplus. com Page 15 www. Vidyarthiplus. com (b) Reactions at the supports. Draw the BMD and SFD also. Use Moment distribution method. 13. A continuous beam ABCD consists of three spans and is loaded as shown in figure. Ends A and D are fixed. Determine the bending moments at the supports and plot the bending moment diagram. 14. Analyze the rigid frame shown in figure. 13. Analyze the continuous beam loaded as shown in figure by the method of moment distribution.

Sketch the bending moment and shear force diagrams. www. Vidyarthiplus. com Page 16 www. Vidyarthiplus. com 14. Analyze the structure loaded as shown in figure by moment distribution method and sketch the bending moment and shear force diagrams. 15. A continuous beam ABCD covers three spans AB = 1. 5L, BC = 3L, CD=L. It carries uniformly distributed loads of 2w, w and 3w per metre run on AB, BC, CD respectively. If the girder is of the same cross section throughout, find the bending moments at supports B and C and the pressure on each support. Also plot BM and SF diagrams. 6. An encastre beam of span L carries a uniformly distributed load w. The second moment of area of the central half of the beam is I1 and that of the end portion is I2. Neglecting the weight of the beam itself find the ratio of I2 to I1 so that the magnitude of the bending moment at the centre is one-third of that of the fixing moments at the ends. 17. A three hinged parabolic arch of 20m span and 4 m central rise carries a point load of 4kN at 4m horizontally from the left hand hinge. Calculate the normal thrust and shear force at the section under the load.

Also calculate the maximum BM Positive and negative. www. Vidyarthiplus. com Page 17 www. Vidyarthiplus. com 18. A parabolic arch, hinged at the ends has a span of 30m and rise 5m. A concentrated load of 12kN acts at 10m from the left hinge. The second moment of area varies as the secant of the slope of the rib axis. Calculate the horizontal thrust and the reactions at the hinges. Also calculate the maximum bending moment anywhere on the arch. 13. Analyse the continuous beam shown in figure by moment distribution method and raw the BMD. 14. Analyse the portal frame ABCD fixed at A and D and has rigid joints at B and C. the column AB is 3m long and column CD is 2m long. The Beam BC is 2 m long and is loaded with UDL of intensity 6 KN/m. The moment of inertia of AB is 2I and that of BC and CD is I. Use moment distribution method. www. Vidyarthiplus. com Page 18 www. Vidyarthiplus. com 16. Draw the shear force and bending moment diagram for the beam loaded as shown in figure. Use moment distribution method. www. Vidyarthiplus. com Page 19

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