INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

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1 INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad CIVIL ENGINEERING TUTORIAL QUESTION BANK Course Name : STRUCTURAL ANALYSIS -I Course Code Class Branch : A405 : II B. Tech II Semester : Civil Engineering Year : Course Faculty : Ms. K. Varsha Reddy Assistant Professor OBJECTIVES To meet the challenge of ensuring excellence in engineering education, the issue of quality needs to be addressed, debated and taken forward in a systematic manner. Accreditation is the principal means of quality assurance in higher education. The major emphasis of accreditation process is to measure the outcomes of the program that is being accredited. In line with this, Faculty of Institute of Aeronautical Engineering, Hyderabad has taken a lead in incorporating philosophy of outcome based education in the process of problem solving and career development. So, all students of the institute should understand the depth and approach of course to be taught through this question bank, which will enhance learner s learning process.. To introduce design concept and process of structures. 2. To review analysis of statically determinate structures. 3. To understand the deformations of structures under loading. 4. To introduce flexibility method for analysis of statically indeterminate structures. 5. To introduce stiffness method for analysis of statically indeterminate structures. PART A (SHORT ANSWER QUESTIONS) S. No Question UNIT I Blooms Taxonomy Define static indeterminacy 2 Explain different types of indeterminacies 3 Explain internal indeterminacy 4 Define Tension Coefficient 5 State Kinematic indeterminacy

2 S. No Question Blooms Taxonomy 6 Write different methods for computing deflection of determinate beam 7 Define Internal Stability 8 What are the different types of frames based on stability What are the different types of frames and explain the same with neat 9 diagrams 0 Define External stability Define Degree of Indeterminacy 2 What is equilibrium condition To find degree of indeterminacy of structures as given below 3 To find degree of indeterminacy of structures as given below 4 5 Differentiate between method of joints & method of sections 6 Explain a pin-jointed frame with a sketch 7 Define a redundant force. 8 What is a portal frame? 9 What are the assumptions made in finding out the forces in a frame? 20 Explain briefly about tension coefficient method. UNIT II Define term deflection of a beam. 2 State conjugate beam theorem 3 Write relation between load, shear force and bending moment acting on a structure 4 State moment area theorems 5 Define strain energy 6 State the castaglianos theorem A steel rod has a square cross section of 0mm x 0mm and a length of,2 7 2M. Calculate strain energy when a stress of 400 Mpa is produced by stretching it. Take E = 200 Gpa 8 Calculate Strain energy due to shear stress for a member which has a length of 0.5M, 20mm Diameter and a pull of 5KN. Take E = 200 Gpa.,2 9 What is the temperature effect on three hinged arches 0 How three hinged arch is different from two hinged arch and explain it

3 S. No Question Blooms Taxonomy What are temperature stresses? Explain 2 Define Force, Work, energy 3 State Eddy s Theorem 4 What is degree of static indeterminacy of a three hinged and two hinged arch? 5 Give expression for strain energy due to axial force 6 Give expression for strain energy due to bending moment 7 Give expression for strain energy due to shear deformation. 8 Define radial shear and normal thrust 9 Give the equation for a parabolic arch whose springing is at different levels? 20 Define linear arch 2 3 UNIT III What are the reaction values for propped cantilever beam when it carries point load? Calculate maximum bending moment for a propped cantilever beam which carries a udl of 0Kn/m for a span of 2m Calculate point of contra flexure for propped cantilever beam has a 4m length carries point load of 20KN at free end 4 Difference between cantilever beam and propped cantilever beam 5 Calculate deflection at mid span for a propped cantilever beam of load 0Kn/m for a span of 4m 6 What is the effect of sinking of support for fixed beam 7 What is effect of rotation 8 Calculate slope and deflection for a fixed beam of load 0Kn/m for a span of 4m 9 Difference between propped cantilever beam and fixed beam 0 A fixed beam of length 3m is subjected to two point loads 9KN at the middle third point. Calculate Bending moment at the fixed end.,2 What is a propped cantilever? 2 What is a Fixed beam? 3 What are the reaction values for propped cantilever beam when it carries uniformly distributed load?,2 4 What is point of contra flexure? 5 Define prop. 6 What are the reaction values for fixed beam when it carries point load?,2 7 What are the reaction values for fixed beam when it carries uniformly distributed load? 8 Define deflection. 9 Define slope. 20 Give boundary conditions for a propped cantilever beam.

4 S. No Question Blooms Taxonomy UNIT IV State Clapeyron s three moment theorem and write equation also. 2 What is the effect of sinking of support in Three moment theorem 3 Explain Continuous beam with neat diagram 4 Derive Slope deflection equation in continuous beam 5 What is the effect of sinking of support in slope deflection method Define stiffness and relative stiffness of a member with different 6 far end conditions 7 Define Carry over factor Define Distribution factor and its importance at fixed end and simply 8 support end 9 Define Elastic curve 0 Importance of Elastic curves in beams. Write down the equilibrium equations used in slope deflection method? 2 What is the basic assumption made in slope deflection method? 3 What is the moment at a hinged end of a simple beam? 4 Write down the slope deflection equation for fixed end support? What are the quantities in terms of which the unknown moments are 5 expressed in slope deflection method? Say true or false and if false, justify your answer slope deflection 6 method is a force method? 7 What are the reasons for sway in portal frames? 8 What are the sign conventions used in slope deflection method? 9 State the limitations of slope deflection method? Write the fixed end moments for a beam carrying a central clockwise 20 moment? Explain the term Focal Length. 2 Define Influence Line. 3 List out the uses of Influence lines. 4 State Muller Breslau s Principle. 5 Where do you get rolling loads in practice UNIT V 6 What is meant by absolute maximum bending moment in a beam

5 S. No Question 7 Where do you have the absolute maximum bending moment in a simply supported beam when a series of wheel loads cross it 8 What do you understand by the term reversal of stresses 9 0 State the location of maximum shear force in a simple beam with any kind of loading. What is the absolute maximum bending moment due to a moving udl longer State Maxwell-Betti s theorem 2 What is meant by maximum shear force diagram? State the location of maximum shear force in a simple beam wit h any kind of loading? Where do you have the absolute maximum bending moment in a simply supported beam when a series of wheel loads cross it? Name the type of rolling loads for which the absolute maximum bending moment occurs at the mid span of a beam? 6 Where do you get rolling loads in practice? 7 What is the absolute maximum bending moment due to a moving udl longer than the span of a simply supported beam? 8 What is meant by absolute maximum bending moment in a beam? 9 Draw influence lines for support reactions in a simply supported beam? 20 What do you understand by an influence line for bending moment? Blooms Taxonomy PART B (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) UNIT I Differentiate between pin-jointed and rigid jointed plane frames Analyze 2 Using method of Tension Coefficient analysis, determine the forces in the members of the plane truss shown in fig.,2 3 Fig shows the plan of a tripod ; the feet P, Q, R being in the horizontal plan and the apex S being 4m above the plane Horizontal loads of 25kN and 200kN are applied at D as shown. Find the forces in all the members assuming that all the joints are pin joints.

6 4 Analyze the plane truss shown in figure using the method Tension Coefficients and find the forces in the members. 5 Using the Method of joints the cantilever, plan truss shown in figure. Find the member forces. 6 Calculate the forces in members of pin jointed space truss shown in figure, using Tension Coefficient method. 7 Each bar of the truss shown in fig 2 has a cross section of 625mm2. Calculate the horizontal deflection of the joint C. use method of joints

7 8 A portal frame ABCD is hinged at A&D and has rigid joints. The frame is loaded as shown in Fig. Analyze the frame using minimum strain energy method. Plot the bending moment diagram. 9 Determine the vertical and horizontal deflections of the free end of the lamp post shown in fig.. Take EI = 6000kN- m2. 0 Determine the vertical and horizontal deflection at the free end of the bent shown in fig. 4. Use the unit load method. Assume uniform flexural rigidity EI throughout. Determine the force in the members of the truss shown in figure. The cross sectional area of vertical and horizontal members is 4000mm2 and that of the diagonal is 6000 mm2. Use method of joints

8 Find the forces in the members of truss shown in figure. The cross sectional area and young s modulus of all the members are the same. Use method of joints 2 Find the forces developed in all the members of truss shown in fig, if the temperature of member AC goes up by 20 c. Take the co efficient of thermal expansion α=2x0-6/ c. Cross sectional area of all the members is 2500mm2 and young s modulus is 200KN/mm2. Use method of joints 3 Determine the force in the members of the truss shown in figure. The cross sectional area of vertical and horizontal members is 4000mm2 and that of the diagonal is 6000 mm2. Use method of sections 4 5 Find the forces in the members of truss shown in figure. The cross sectional area and young s modulus of all the members are the same. Use method of sections

9 Find the forces developed in all the members of truss shown in fig, if the temperature of member AC goes up by 20 c. Take the co efficient of thermal expansion α=2x0-6/ c. Cross sectional area of all the members is 2500mm2 and young s modulus is 200KN/mm2. Use method of sections 6 Determine the force in the members of the truss shown in figure. The cross sectional area of vertical and horizontal members is 4000mm2 and that of the diagonal is 6000 mm2. Use tension coefficient method 7 Find the forces in the members of truss shown in figure. The cross sectional area and young s modulus of all the members are the same. Use tension coefficient method 8 9 Find the forces developed in all the members of truss shown in fig, if the temperature of member AC goes up by 20 c. Take the co efficient of thermal expansion α=2x0-6/ c. Cross sectional area of all the members is 2500mm2 and young s modulus is 200KN/mm2. Use tension coefficient method

10 20 A two span continuous truss is loaded as shown. All the members are of the same material and have the same cross sectional area. Find the reaction at the central support C. also find the forces in all the members AB, BF, FG, HI, GI, GD of the truss. UNIT - II A circular three hinged arch of span 25m with a central rise of 5m is hinged at the crown and the end supports. It carries a point load of 00 kn at 6m from the left support. Calculate i. The reaction at the supports ii. Moment at 5m from the left support. 2 A three hinged circular arch of span 6m and rise 4m is subjected to two point loads of 00 kn and 80 kn at the left and right quarter span points respectively. Find the reaction at the supports. Find also the bending moment, radial shear and normal thrust at 6m from left support. 3 A symmetrical three hinged arch has a span of 50 & rise 5m. Find the maximum bending moment at a quarter point of the arch caused by a uniformly distributed load of 0kN/m which occupies any portion of the span. Indicate the position of the load for this condition. 4 A three hinged parabolic arch of span 30m and rise 5m carries a uniformly distributed load of 40kN per meter on the whole span and a point load of 200kN at a distance of 5m from the right end. Find the horizontal thrust, resultant reaction, bending moment and normal thrust at a section 5m from the left end. 5 A three hinged parabolic arch has supports at different levels having span 20m and carries a UDL of 30kN/m over the left half of the span. The left support is 5m below the crown and the right support is 4m below the crown. Draw the BMD. Also find the normal thrust and radial shear at a section 4m from the left support. Apply, Analyze and 6 Explain briefly about strain energy in elastic system. 7 Derive expression for strain energy 8 Derive expression for strain energy due to axial load. 9 Derive expression for strain energy due to bending

11 0 Derive expression for strain energy due to shear deformation. Explain unit load method. 2 Write short notes on strain energy. 3 Calculate the deflection at centre o a simple beam ACB subjected to varying load of zero from A to w kn/m at C and zero at B. Take EI as constant. 4 Define arch. What are the applications of arches? 5 Explain the different types of arches. 6 State and explain eddy s theorem. 7 Write short notes on analysis of three hinged arches. 8 Explain about linear arch. 9 Why is a arch preferred over a straight beam? Explain. 20 Explain why the moment is zero at all points in a three hinges parabolic arch. UNIT - III A cantilever of length 0 m carries udl of 800N/m length over the whole length. The free end of the cantilever is supported on a prop. The prop sinks by 5mm. If E=3X05N/mm2 and I=0 8 mm 4, then the prop reaction 2 A cantilever of length 8m carries udl of 2Kn/m run over the whole length. The cantilever is propped rigidly at the free end. If E=X05N/mm2 and I=0 8 mm 4, then determine reaction at the rigid prop and deflection at the center 3 A cantilever of length 5m carries a point load of 24kn at its center. The cantilever is propped rigidly at the free end. Determine the reaction at the rigid prop. 4 A cantilever of length 4m carries a UDL of Kn/m run over the whole span length. The cantilever is propped rigidly at the free end. If the value of If E=2X05N/mm2 and I=0 8 mm 4, Determine the reaction at the rigid prop and deflection at the center. 5 A cantilever of length 8 m carries UDL of 0.8Kn/m length over the whole length. The free end of the cantilever is supported on a prop. The prop sinks by 5mm. If E=2X05N/mm2 and I=0 8 mm 4, then the prop reaction 6 A fixed beam AB, 5m long, carries a point load of 48kn at its center. the moment of inertia of the beam is 5x07 mm4 and value of E for the beam materials is 2x05 N/mm2. Determine Fixed end moments at A and B, and Deflection under the load. Understanding, Analyze & Evaluate 7 A fixed beam of length 5m carries a point load of 20KN at a distance of

12 2m from A. Determine the fixed end moments and deflection under the load, if the flexural rigidity of the beam is x04 Kn/m2 8 A fixed beam of length 6m carries point loads of 20kn and 5kn at distance 2m and 4m from the left end A. Find the fixed end moments and the reactions at the supports. Draw B.M and S.F diagrams. 9 A fixed beam of length 3m carries tow point loads of 30kn each at a distance of m from both ends. Determine the fixing moments and draw B.M diagram. 0 A fixed beam AB of length 6m carries a uniformly distributed load 3kn/m over the left half of the span together with a point load of 4kn at a distance of 4.5m from the left end. Determine the fixing end moments and support reactions. A fixed beam of span L is subjected to UDL throughout w/m. What is end moments and moment at the centre? Draw SFD and BMD for a propped cantilever beam span L subjected to 2 UDL throughout w/m Draw SFD and BMD for a propped cantilever beam span L subjected to 3 point load at free end. Draw the SF and BM Diagrams (qualitative) of a fixed beam of L m long 4 carries a point load W at the midpoint. For the propped cantilever shown in fig. Calculate the BM A cantilever of length 6m carries a point load of 48 kn at its centre. The cantilever is propped rigidly at the free end. Determine the reaction at the rigid prop. A fixed beam AB of length 6m carries point loads of 60 kn and 20kN at a distance of2m and 4m from the left end A. Find the fixed end moments and the reactions at the supports. Draw BM and SF diagrams A fixed beam of 8m span carries a UDL of 40 kn/m run over 4m length starting from left end and a concentrated load of 80kN at a distance of 6m from the left end. Find 8 i. Moments at the supports. ii. Deflection at centre of the beam 9 20 Take EI = 5000 knm2 A fixed beam of 6m length is loaded with two equal point loads of 50kN each at distance of 2m from each support. Draw the BMD and SFD. E = 2 x 08 kn/m2, I = 8 x 08 mm4. A fixed beam of span 8 m carries an udl of 2 kn/m over a length of 4 m from the left support and a concentrated load of 0 kn at a distance of 6m from the left support. Find the fixed end moments and draw the B.M. and S.F. diagrams UNIT - IV

13 A 3-span continuous beam ABCD has fixed end supports. On end span AB= 6m there is u.d.l. of 20 kn/m, while on CD = 5 m there is a point load of 80 kn at mid span on the central span BC = 5 m, there is a point Analyze & load of 50kN at 3m from B. If the moment of inertia of BC is twice that of AB and CD analyse by moment distribution method and sketch the B.M.D 2 If support B of the continuous beam of Question No. settles by 30 mm, obtain the support moments by slope deflection method, taking I = 400 cm4 and E= 2 05 N/mm2. Sketch the B.M.D. 3 Using Slope Deflection method obtain the support moments for the 2- span continuous beam shown below. Sketch BMD. 4 Using Claperoyn s method finds the support movements for the 2-span continuous beam loaded as shown below figure 2. Sketch the B.M.D. 5 Using moment distribution method, analyse the 2-span continuous beam ABC, having end supports A and C fixed. There is a load of 5 kn in span AB=5 m at 3 m from A, while on span BC there is a load of 8 kn at 2.5 m from C. Sketch the B.M.D 6 If the end spans A and C of the beam given in Question No.2 are simply supported analyse using slope deflection method. Sketch the BMD. 7 Analyze two span continuous beam ABC in which support B sinks by 5mm by slope deflection method. Then draw Bending moment & Shear force diagram. Take EI constant and draw Elastic curve. 8 Analyze continuous beam ABCD by slope deflection method and then draw bending moment diagram. Take EI constant.

14 9 Analyse the continuous beam ABCD shown in figure by slope deflection method. The support B sinks by 5mm. Take E=200x05 KN/m2 and I=20x06m4 0 Three span continuous beam ABCD is fixed at A and continuous over B, C and D. The beam subjected to loads as shown. Analyse the beam by slope deflection method and draw bending moment and shear force diagram A Continuous beam ABCD fixed at A and D and continuous over supports B and C. The span AB=5m carries a central concentrated load of 0kN. The span BC=4m carries a uniformly distributed load of 4 kn/m over the entire span of BC. The span CD=6m carries a non central concentrated load of 8 kn acting at a distance of 2m from the end D. Analyze the beam and draw bending moment diagram using slope deflection method. A Continuous beam ABCD fixed at A and D and continuous over supports B and C. The span AB=5m carries a central concentrated load of 0kN. The span BC=4m carries a uniformly distributed load of 4 kn/m over the entire span of BC. The span CD=6m carries a non central concentrated load of 8 kn acting at a distance of 2m from the end D. Analyze the beam and draw bending moment diagram using moment distribution method. A continuous beam ABC consist of span AB=3m and BC=4m, the ends A and C being fixed. AB and BC carry uniformly distributed loads of intensity 4kN/m and 5kN/m respectively. Find the support moments and draw the bending moment diagram for the beam using slope deflection method. The beam is of uniform section throughout. A continuous beam ABC consist of span AB=3m and BC=4m, the ends A and C being fixed. AB and BC carry uniformly distributed loads of intensity 4kN/m and 5kN/m respectively. Find the support moments and draw the bending moment diagram for the beam using moment distribution method. The beam is of uniform section throughout. Analyze the beam shown in fig. by slope deflection method and draw the SFD and BMD.EI=Constant.

15 6 Analyze the beam shown in fig. by moment distribution method and draw the SFD and BMD.EI=Constant. 7 Analyze the continuous beam ABCD shown in fig. by slope deflection method.take EI=Constant. Also sketch the shear force and Bending Moment diagram. 8 Analyze the continuous beam ABCD shown in fig. by moment distribution method.take EI=Constant. Also sketch the shear force and Bending Moment diagram. 9 Analyze the continuous beam shown in fig. by slope deflection method. Support B settles by 8mm and C settles by 2 mm. I=60000cm4, E=20x06kN/m2.Draw the SFD and BMD. 20 Analyze the continuous beam shown in fig. by moment distribution method. Support B settles by 8mm and C settles by 2 mm. I=60000cm4, E=20x06kN/m2.Draw the SFD and BMD. UNIT - V Two point loads of 25kN and 250kN spaced 4m in figure, apart cross a girder of 7.5m from left to right with the 25kN load leading. Draw the influence line for the bending moment and find the value of maximum bending moment at a section C, 7.5m from the left hand support. Also find the absolute maximum bending moment due the given load system. Analyze

16 Figure 2 Four wheel load of 7,5,9 & 6 kn cross a girder of span 22.5m from the left to right followed by an UDL of 5kN/m of 4m length. The 7kN load is leading. The spacing between the loads are shown in fig 2. The head of UDL is 3m from the last load of 6kN. Using influence lines calculate the shear force and bending moment at a section 8m form the left support when the 5kN load is at the center of span. Figure 2 3 Draw the influence line diagrams for the forces in the members P, Q, & R of the truss shown in fig 3. Figure 3 4 Draw the influence lines for the members UU2,, L2L3, U3L3, & U4L4 of the deck type girder shown in figure 4. 5 Sketch the influence line diagram for S.F. and B. M. at 4 m from the left end of a simply-supported girder of span 0 m. Hence find the maximum S.F. and maximum B.M. at the section if two wheel loads of 8 kn and 6 kn spaced 2 m apart move from left to right. 6 Illustrate the procedure to find the forces in the members of a Pratt truss due to moving loads using the influence line diagrams. 7 A UDL of intensity 0 kn/m and 4 m long crosses a simply supported girder of 2 m span. Sketch the I.L. diagrams for S.F. and B.M. at /3

17 span. Hence find the maximum S.F. and B.M. at the section. Find also the absolute maximum S.F. and B.M. 8 A UDL of intensity 20 kn/m and 5 m long crosses a simply supported girder of 5 m span. Sketch the I.L. diagrams for S.F. and B.M. at mid span. Hence find the maximum S.F. and B.M. at the section. Find also the absolute maximum S.F. and B.M. 9 Sketch the influence line diagram for S.F. and B. M. at 5 m from the right end of a simply-supported girder of span 5 m. Hence find the maximum S.F. and maximum B.M. at the section if two wheel loads of 0 kn and 8 kn spaced 4 m apart move from left to right. 0 Four wheel load of 4, 6, 8, 6 and 4 kn cross a girder of span 25m from the left to right. The 0 kn load is leading. The spacing between each load is 2.5m. Using influence lines calculate the shear force and bending moment at a section 8m form the left support when the 8 kn load is at the center of span. A system of four loads 80, 60, 60 and 20 kn crosses a simply supported beam of span 25m with the 20 kn load leading. The loads are equally spaced at m. Determine the values of the following using influence lines i. Maximum bending moment at a section 0m from left support and ii. ii. Absolute maximum shear force and bending moment in the beam. A beam has a span of 24m, draw the influence line diagram for the bending moment and shear force at a section 8m from the left and also 2 determine maximum bending moment and shear force at this section due to two point loads of 0kN and 6kN at a fixed distance of 2m apart rolling from left to right with 6kN load leading A simply supported beam has a span of 6m,is subjected to a UDL(dead load) of 5kN/m and a UDL(live load) of 8kN/m (longer than the span) 3 travelling from left to right. Draw the ILD for shear force and bending moment at a section 4m from left end. Use these diagrams to determine the maximum shear force and bending moment at this section. Draw the influence line for M B for the continuous beam ABC simply 4 supported at A and C using Muller Breslau`s principle. AB=3m, BC=4m.EI is constant. Draw the influence line diagram for the propped reaction of a propped 5 cantilever beam having span 6m. EI=Constant. Determine the influence line diagram for bending moment at a point D, the middle point of span AB of a continuous beam ABC of span AB=6m 6 and BC=4m simply supported at supports A,B and C. Compute the ordinates at every m interval. The warren girder of 25m span is made of 5 panels of 5m each. The diagonals are inclined at 60 to the horizontal. Draw the influence line 7 diagram for force in upper chord member in the second panel from left. Hence the forces in it when there is load of 60 kn at each lower joint. Draw the influence line for R A for the continuous beam ABC of span AB = 8 BC = 4m simply supported at A, B &C. Compute the ordinates at every m interval, EI = constant

18 A system of four loads 40, 80, 80 and 60 kn crosses a simply supported beam of span 20m with the 60 kn load leading. The loads are equally spaced at m. Determine the values of the following using influence 9 lines. i. Maximum bending moment at a section 8m from left support and ii. ii. Absolute maximum shear force and bending moment in the beam. Draw the influence line for R A for the continuous beam ABC of span AB = 20 BC = 6m simply supported at A, B &C. Compute the ordinates at every.5m interval, EI = constant PART C (ANALYTICAL QUESTIONS) UNIT I What are the different methods for analysis of Frames? Write the assumptions made in analyzing perfect frame. 2 Determine the forces in the members of the cantilever truss shown in fig. method of joints Understanding,2 3 For the truss shown in Fig, Determine reactions at the two supports P and Q and forces in the members using method of joints 4 Find the forces in the members of truss shown in fig. using method of joints

19 5 In the cantilever truss shown in fig. Calculate reaction at A using method of joints 6 Calculate force in the member BC for truss shown in fig. 7 Determine the forces in all the members of a truss shown in fig below by method of joints.

20 8 Find the force in all members of the truss shown in Figure 2.55 by method of joints. 9 Determine the forces in all the members of a truss shown in fig below by method of sections. 0 Find the force in all members of the truss shown in Figure 2.55 by method of sections.

21 Determine the forces in the members of the cantilever truss shown in fig. method of sections For the truss shown in Fig, Determine reactions at the two supports P and Q and forces in the members using method of sections 2 Find the forces in the members of truss shown in fig. using method of sections 3 4 In the cantilever truss shown in fig. Calculate reaction at A using method of sections

22 Determine the forces in the members of the cantilever truss shown in fig. using tension coefficient method 5 For the truss shown in Fig, Determine reactions at the two supports P and Q and forces in the members using tension coefficient method 6 7 Find the forces in the members of truss shown in fig. using tension coefficient method

23 In the cantilever truss shown in fig. Calculate reaction at A using tension coefficient method 8 Determine the forces in all the members of a truss shown in fig below by tension coefficient method 9 Find the force in all members of the truss shown in Figure 2.55 by tension coefficient method 20

24 UNIT - II The strain energy due to bending in the cantilever beam shown in fig. Analyze & 2 The strain energy stored in member AB of the pin joined truss shown in fig. 3 A simply supported beam of span l and flexural rigidity EI carries a unit point load at its center. What is the strain energy in the beam due to bending? 4 Calculate the strain energy stored in a simply supported beam of span l and flexural rigidity EI due to central concentrated load W 5 If the strain energy absorbed in a cantilever beam in bending under its own weight is K times greater then the strain energy absorbed in an identical simply supported beam in bending under its own weight, the then what could be the magnitude. 6 A three hinged arch is shown in fig. Calculate horizontal thrust. 7 A three hinged arch parabolic arch ABC has a span o 20m and central rise of 4m. The arch has hinges at the ends and at the center. A train of two point loads of 20Kn and 0Kn, 5m apart, crosses this arch from left to right, with 20Kn load leading. Calculate maximum thrust induced at the support. 8 For the three hinged parabolic arch shown in fig what is the value of horizontal thrust.

25 9 Calculate horizontal thrust at support A in a three hinged arch shown in fig. 0 A three hinged semicircular arch of radius R carries a uniformly distributed load W per unit run over the whole span. What will be the horizontal thrust? An axial pull of 40 kn is suddenly applied to a steel rod 2m long and 000mm2 in cross section. Calculate the strain energy that can be absorbed if E = 200 GN/m2. A cantilever of rectangular section breadth b, depth d and of length l carries uniformly distributed load spread from free end to the mid 2 section of the cantilever. Using Castigliano s theorem find: Slope and deflection due to bending at the free end. A beam 4m in length is simply supported at the ends and carries a 3 uniformly distributed load of 6 kn/m length. Determine the strain energy stored in the beam. Take E = 200 GPa and I = 440 cm4 A beam simply supported over a span of 3m carries a UDL of 20 kn/m over the entire span. The flexural rigidity EI = 2.25 MNm2 Using 4 Castigliano s theorem, determine the deflection at the centre of the beam. For the beam shown in fig. find the slope and deflection at C. 5 6 For the truss shown in fig. find the total strain energy stored. E : 2 05 N/mm2; Area : AB : 00 mm2; BC : 00 mm2; AC : 80 mm2;

26 Compare the bending moments of a three hinged arch ACB of span L, rise h, hinged at crown C and carrying a point load P at a distance L/4 from A with a straight beam carrying same load. Show that the bending moment of a three hinged parabolic arch carrying a uniformly distributed load is zero at any cross section. A three hinged circular arch of span 20m and rise 5m is subjected to two point loads of 50 kn and 00 kn at the left and right quarter span points respectively. Find the reaction at the supports. Find also the bending moment, radial shear and normal thrust at 8m from left support. A symmetrical three hinged arch has a span of 60 & rise 6m. Find the maximum bending moment at a quarter point of the arch caused by a uniformly distributed load of 5kN/m which occupies any portion of the span. Indicate the position of the load for this condition. UNIT - III A cantilever ABC of length is fixed at the end A and is simply supported at an intermediate support B. The cantilever carries a uniformly distributed load w/unit length over the whole span. Determine the position of the support B so that reactions at A and B are equal. 2 A beam AB of length L, simply supported at the ends and propped at mid span, carries a udl of w per unit length. Calculate the prop reaction and plot the bending moment diagram. 3 A cantilever of uniform cross section carries a udl w/unit length. What upward force must be applied at the end to reduce the deflection there to zero? 4 For the propped beam shown in Fig. Determine the reaction R and sketch the shear force and bending moment diagrams. Analyze & 5 A 5m long fixed beam AB is hinged at the point H, 3M from the end A, thus forming two concentrated cantilever AH and BH. A load of 86Kn acts at a distance of 2m from the left end A. Find the reaction at the hinge and the fixing moments at A and B. Takes IAH=2IBH. 6 A fixed-ended beam of 9m span carries udl of 5Kn/m (including its own weight) and two pint loads of 200kn at the third point in the span. Assuming rigid end fixing. Find the fixing moment.

27 7 For a rigidly fixed beam AB of 5m span carrying udl of 0Kn/m, over the entire span, locate the points of contraflexure and draw the S.F and B.M diagrams. 8 A beam built in at both the ends is loaded with a triangular loading on its one half of the span, the other load half carries no load. The load gradually increases from zero at the fixed end to 5Kn/m at mid span. The span of the beam is 5m. Determine the bending moments. 9 A beam of uniform cross section and 5m length, is built in at each end. It carries a udl of 0Kn/m extending from 3m from one end and a concentrated load of 20Kn, m from the other end. Sketch the B.M diagram giving principal numerical values. 0 A beam fixed at both ends is prismatic. It carries a load of varying intensity zero at the end to w/unit length at the center. Determine the fixed moments. A fixed beam AB of 8m span carries a point load of 00 kn at its mid span and a uniformly distributed load of 20 kn/m throughout its entire span. Find the following: (i) Fixing moments at the ends and (ii) Reactions at the supports Also draw the SF and BM diagrams. What are the fixed end moments for a fixed beam of length l subjected 2 to a concentrated load 2W at a distance a from left end. Derive a relation fro prop reaction for a simply supported beam with 3 uniformly distributed load and propped t the centre. A Steel fixed beam AB of span 6 m is 60 mm wide and 00 mm deep. The 4 support B sinks down by 6 mm. Fine the fixing moments at A and B. Take E = 200 GPa. Derive and sketch the shear force, bending moment and deflection of a 5 propped cantilever beam subjected o udl over the entire span. What are the advantages and disadvantages of a fixed beam? A fixed beam AB of length 3m is having moment of inertia I=3 x 06 mm4 the support B sinks down by 3mm. If E = 2 x 05 N/mm2. Find the fixing moments For the fixed beam shown in fig. what is the fixed end moment at A and B Draw BMD for a propped cantilever beam span 2L subjected to UDL throughout w/m. A fixed beam of span L is subjected to UDL throughout 2w/m. What is end moments and moment at the centre? UNIT - IV A continuous beam ABC consists of two consecutive spans of 4m each and carries a distributed load of 60Kn/m run. The end A is fixed and the end C simply supported. Find the support moments and the reactions. Analyze & 2 Analyze the continuous beam shown in fig, if the support B sinks by cm.

28 The section is constant throughout. E=200Gpa and I=8500cm4. 3 Draw S.F and B.M diagrams for a continuous beam loaded as shown I fig. 4 A continuous beam ABCD 20m long is continuous over 3 spans. AB=8m, BC=4m, CD=8m. Moment of inertia is 2I, that of BC is I and that of CD is 2I. There is a UDL load of 500 N/m over spans AB and BC. On the span CD there is a central load of 4000N. The ends are fixed and during loading the support B sinks by cm. Find the fixed end moments using slope deflection method. I=600cm4 and E=200GPa 5 A continuous beam ABCD 8m long is continuous over 3 spans. AB=8m, BC=4m, CD=8m. Moment of inertia is constant over the whole span. A concentrated load of 4000N is acting of AB at 3m from support A. There is a UDL load of 000 N/m on BC. On the span CD there is a central load of 4000N. The ends are fixed and during loading the support B sinks by cm. Find the fixed end moments using slope deflection method. I=600cm4 and E=200GPa 6 Analyze the continuous beam ABCD 3l long using slope deflection method is continuous over 3 spans with a uniformly distributed load of w per unit length. AB=BC=CD=l. The beam is of constant section throughout its length and supports remain at same level after loading. 7 A continuous beam ABCD 20m long is continuous over 3 spans. AB=8m, BC=4m, CD=8m. Moment of inertia is 2I, that of BC is I and that of CD is 2I. There is a UDL load of 500 N/m over spans AB and BC. On the span CD there is a central load of 4000N. The ends are fixed and during loading the support B sinks by cm. Find the fixed end moments using slope deflection method. I=600cm4 and E=200GPa 8 A continuous beam ABCD 8m long is continuous over 3 spans. AB=8m, BC=4m, CD=8m. Moment of inertia is constant over the whole span. A concentrated load of 4000N is acting of AB at 3m from support A. There is a UDL load of 000 N/m on BC. On the span CD there is a central load of 4000N. The ends are fixed and during loading the support B sinks by cm. Find the fixed end moments using slope deflection method. I=600cm4 and E=200GPa 9 Analyze the continuous beam ABCD 3l long using slope deflection method is continuous over 3 spans with a uniformly distributed load of w per unit length. AB=BC=CD=l. The beam is of constant section throughout its length and supports remain at same level after loading. 0 A continuous beam ABCD 8m long is continuous over 3 spans. AB=8m, BC=4m, CD=8m. Moment of inertia is constant over the whole span. A

29 concentrated load of 4000N is acting of AB at 3m from support A. There is a UDL load of 000 N/m on BC. On the span CD there is a central load of 4000N. The ends are fixed and during loading the support B sinks by cm. Analyze using elastic curve. I=600cm4 and E=200GPa A continuous beam ABCD of uniform cross-section is loaded as shown in Figure Find the following: (i) Bending moments at the supports; (ii) Reactions at the supports. Also draw BM and SF diagrams. A continuous beam ABCD in shown in Fig. Draw SFD and BMD indicating the salient points. (AUC Nov/Dec 20) 2 Draw the S.F. and B.M. diagrams for the beam shown in the fig. Use three moment equation. (AUC Apr/May 202) A fixed beam AB of length 8m carries point loads of 50 kn and 20kN at a distance of 3m and 4m from the left end A. Find the fixed end moments and the reactions at the supports. Draw BM and SF diagrams A continuous beam ABC 8m long consists of two spans AB = 4m and BC = 5m. The span AB carries a load of 80 kn/m while the span BC carries a load of 30 kn/m. Find the support moments and the reactions at the supports. A fixed beam of span 8 m carries an udl of 4 kn/m over a length of 4 m from the left support and a concentrated load of 20 kn at a distance of 6m from the left support. Find the fixed end moments and draw the B.M. and S.F. diagrams. Analyse the following beam. 7

30 Draw the S.F. and B.M. diagrams for the beam shown in the fig. 8 For the fixed beam shown in fig. what is the fixed end moment at A and B A fixed beam of span 2L is subjected to UDL throughout w/m. What is end moments and moment at the centre? UNIT - V For simply support beam 0M, I.L.D is drawn for B.M at a section 4m from the let hand support. The maximum B.M at the section due to moving load of 60KN, is equal to 2 A udl of 30Kn/m and 4m length rolls over a span of 6M. The absolute maximum B.M in KN-M is 3 A number of wheel loads 3t, 4t, 5t and 6t spaced 2m, 3m and 3m respectively with the 3t load leading from left to right. To find the maximum B.M at 8m from A, what load must be placed at what section? 4 Three wheel loads 0t, 26t and 24t spaced 2m apart roll on a girder from left to right with the 0t load leading. The girder has a span of 20m. For the condition of maximum bending moment at a section 8m from the left end what load should be placed at the section. 5 A beam PQRS is 8m long and is simply supported at points Q and R 0m apart. Overhang PQ and RS are 3m and 5m respectively. A train of two point loads of 50Kn and 00Kn, 5m apart, crosses this beam from left to right with 00Kn load leading. What is the maximum sagging moment under 50Kn. 6 For above problem the passage of loads, what are the maximum and minimum reactions at support R, in Kn respectively? Analyze & 7 What is the variation of influence line for stresses unction in a statically. 8 What is the shape of influence line diagram for the maximum bending moment is respect of a simply support beam. 9 Five concentrated loads 40Kn, 20Kn, 00Kn and 80Kn spaced at equal distance of 3m between them cross from left to right of a S.S beam of

31 span 40m with the 40Kn load leading. What load gives the maximum bending moment at section C 5m from left? 0 What is the area of influence line diagram for the reaction at the hinged end of a uniform propped cantilever beam of span L? 2 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 () reactions at A, B and C (2) shear to the right of B (3) bending moment at E Construct the influence line for the reaction at supports A and B for the beam of span 0m. The beam structure is shown in Figure Construct the influence line for support reaction at B for the given beam as shown in Fig 3 Construct the influence line for shearing point C of the beam 4 Construct the influence line for the moment at point C of the beam shown in Figure 5 Construct the influence line for the moment at point C of the beam shown in Figure 6 7 Construct the influence line for a) reaction at A and B b) shear at point C c) bending moment at point C of the beam in the figure below.

32 8 Construct the influence line for - the reaction at A, C and E - the shear at D - the moment at D 9 Construct the influence line for a) shear before and after support B b) moment at point B of the beam in the figure below. 20 Construct the influence line for - shear before and after support C - moment at point C Prepared by: K. Varsha Reddy, Assistant Professor HOD, CIVIL ENGINEERING