KINGS COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING Question Bank Sub. Code/Name: CE1303 Structura Anaysis-I Year: III Sem:V UNIT-I DEFLECTION OF DETERMINATE STRUCTURES 1.Why is it necessary to compute defections in structures? Computation of defection of structures is necessary for the foowing reasons: a. If the defection of a structure is more than the permissibe, the structure wi not ook aesthetic and wi cause psychoogica upsetting of the occupants. b. Exessive defection may cause cracking in the materias attached to the structure. For exampe, if the defection of a foor beam is excessive, the foor finishes and partition was supported on the beam may get cracked and unserviceabe. 2.What is meant by cambering technique in structures? Cambering is a technique appied on site, in which a sight upward curve is made in the structure/ beam during construction, so that it wi straighten out and attain the straight shape during oading. This wi consideraby reduce the downward defection that may occur at ater stages. 3.Name any four methods used for computation of defections in structures. 1. Doube integration method 2.Macauay s method 3. Conjugate beam method 4.Moment area method 5. Method of eastic weights 6.Virtua work method- Dummy unit oad method 7. Strain energy method 8.Wiiot Mohr diagram method 4. State the difference between strain energy method and unit oad method in the determination of defection of structures. In strain energy method, an imaginary oad P is appied at the point where the defection is desired to be determined. P is equated to zero in the fina step and the defection is obtained. In unit oad method, an unit oad (instead of P) is appied at the point where the defection is desired. 5. What are the assumptions made in the unit oad method? ` 1. The externa & interna forces are in equiibrium. 2. Supports are rigid and no movement is possibe. 3. The materias is strained we with in the eastic imit. 6. Give the equation that is used for the determination of defection at a given point in beams and frames. Defection at a point is given by, δ I =
0 Where M x = moment at a section X due to the appied oads m x = moment at a section X due to a unit oad appied at that point I and in the direction of thedesired dispacement EI = fexura rigidity 7.Write down the equations for moments due to the externa oad for beam shown in Fig. X1 50KN X 2 X 3 A B R X 1 R B x X2 x X 3 10m Portion Mx Limits AC R A x 0 to 4 CD R A x - 50(x-4) 4 to 5 DB R A x - 50(x-4) 5 to 10 8.Distinguish between pin jointed and rigidy jointed structure. S.no Pin jointed structure Rigidy jointed structure 1. The joints permit change of ange The members connected at a rigid joint wi between connected member. maintain the ange between them even under deformation due to oads. 2. The joints are incapabe of transferring Members can transmit both forces and any moment to the connected members moments between themseves through the and vice-versa. joint. 3. The pins transmit forces between Provision of rigid joints normay increases connected member by deveoping shear. the redundancy of the structures. 9.What is meant by therma stresses? Therma stresses are stresses deveoped in a structure/member due to change in temperature. Normay, determine structures do not deveop therma stresses. They can absorb changes in engths and consequent dispacements without deveoping stresses. 10. What is meant by ack of fit in a truss? One or more members in a pin jointed staticay indeterminate frame may be a itte shorter or onger than what is required. Such members wi have to be forced in pace during the assembing. These are caed members having Lack of fit. Interna forces can deveop in a redundant frame (without externa oads) due to ack of fit.
11. Write down the two methods of determining dispacements in pin jointed pane frames by the unit oad concept. The methods of using unit oads to compute dispacements are, i) Dummy unit oad method. ii) Using the principe of virtua work. iii) 12. What is the effect of temperature on the members of a staticay determinate pane truss. In determinate structures temperature changes do not create any interna stresses. The changes in engths of members may resut in dispacement of joints. But these woud not resut in interna stresses or changes in externa reactions. 13. Distinguish between deck type and through type trusses. A deck type is truss is one in which the road is at the top chord eve of the trusses. We woud not see the trusses when we ride on the road way. A through type truss is one in which the road is at the bottom chord eve of the trusses. When we trave on the road way, we woud see the web members of the trusses on our eft and right. That gives us the impression that we are going` through the bridge. 14. Define static indeterminacy of a structure. If the conditions of statics i.e., ΣH=0, ΣV=0 and ΣM=0 aone are not sufficient to find either externa reactions or interna forces in a structure, the structure is caed a staticay indeterminate structure. 15. Briefy outine the steps for determining the rotation at the free end of the cantiever oaded as shown in Fig. W A B Ans: X W A x B A B 1 a. Mx = -Wx b. m x = -1 X
c. d. θ B = M x m x dx = -Wx) (-1) dx 0 EI 0 EI 16. The horizonta dispacement of the end D of the porta frame is required. Determine the reevant equations due to the unit oad at appropriate point. 4m 30 KN B 3m 3m C E A D
Ans: B X E X C 4m X X X X X A x x 1 Appy unit force in the horizonta direction at D. m x vaues are tabuated as beow: Portion m x Limits DC 1x 0 to 4m CE 1 4 0 to 3m EB 1 4 3 to 6m BA 1x 0 to 4m D 17. Differentiate the staticay determinate structures and staticay indeterminate structures? S.No staticay determinate structures staticay indeterminate structures 1. Conditions of equiibrium are sufficient Conditions of equiibrium are insufficient to to anayze the structure anayze the structure 2. Bending moment and shear force is Bending moment and shear force is dependent independent of materia and cross of materia and independent of cross sectiona sectiona area. area. 3. No stresses are caused due to Stresses are caused due to temperature change temperature change and ack of fit. and ack of fit. 18. Define : Trussed Beam. A beam strengthened by providing ties and struts is known as Trussed Beams. 19. Define: Unit oad method. The externa oad is removed and the unit oad is appied at the point, where the defection or rotation is to found.
20. Give the procedure for unit oad method. 1. Find the forces P1, P2,. in a the members due to externa oads. 2. Remove the externa oads and appy the unit vertica point oad at the joint if the vertica defection is required and find the stress. 3. Appy the equation for vertica and horizonta defection.
1. Where do you get roing oads in practice? UNIT-II INFLUENCE LINES Shifting of oad positions is common enough in buidings. But they are more pronounced in bridges and in gantry girders over which vehices keep roing. 2. Name the type of roing oads for which the absoute maximum bending moment occurs at the midspan of a beam. (i) Singe concentrated oad (ii) ud onger than the span (iii) ud shorter than the span (iv) Aso when the resutant of severa concentrated oads crossing a span, coincides with a concentrated oad then aso the maximum bending moment occurs at the centre of the span. 3. What is meant by absoute maximum bending moment in a beam? When a given oad system moves from one end to the other end of a girder, depending upon the position of the oad, there wi be a maximum bending moment for every section. The maximum of these bending moments wi usuay occur near or at the midspan. The maximum of maximum bending moments is caed the absoute maximum bending moment. 4. Where do you have the absoute maximum bending moment in a simpy supported beam when a series of whee oads cross it? When a series of whee oads crosses a simpy supported beam, the absoute maximum bending moment wi occur near midspan under the oad W cr, nearest to midspan (or the heaviest oad). If W cr is paced to one side of midspan C, the resutant of the oad system R sha be on the other side of C; and W cr and R sha be equidistant from C. Now the absoute maximum bending moment wi occur under W cr. If W cr and R coincide, the absoute maximum bending moment wi occur at midspan. 5. What is the absoute maximum bending moment due to a moving ud onger than the span of a simpy supported beam? When a simpy supported beam is subjected to a moving ud onger than the span, the absoute maximum bending moment occurs when the whoe span is oaded. M max max = w 2 8 6. State the ocation of maximum shear force in a simpe beam with any kind of oading. In a simpe beam with any kind of oad, the maximum positive shear force occurs at the eft hand support and maximum negative shear force occurs at right hand support. 7.What is meant by maximum shear force diagram? Due to a given system of roing oads the maximum shear force for every section of the girder can be worked out by pacing the oads in appropriate positions. When these are potted for a the sections of the girder, the diagram that we obtain is the maximum shear force diagram. This diagram
yieds the design shear for each cross section. 8. What is meant by infuence ines? An infuence ine is a graph showing, for any given frame or truss, the variation of any force or dispacement quantity (such as shear force, bending moment, tension, defection) for a positions of a moving unit oad as it crosses the structure from one end to the other. 9. What are the uses of infuence ine diagrams? (i) Infuence ines are very usefu in the quick determination of reactions, shear force, bending moment or simiar functions at a given section under any given system of moving oads and (ii) Infuence ines are usefu in determining the oad position to cause maximum vaue of a given function in a structure on which oad positions can vary. 10. Draw the infuence ine diagram for shear force at a point X in a simpy supported beam AB of span m. 1 X A B x (-x) (-x) + x/ 11. Draw the ILD for bending moment at any section X of a simpy supported beam and mark the ordinates. A x 1 X (-x) B (-x) 12. What do you understand by the term reversa of stresses? In certain ong trusses the web members can deveop either tension or compression depending upon the position of ive oads. This tendancy to change the nature of stresses is caed reversa of stresses.
13. State Muer-Bresau principe. Muer-Bresau principe states that, if we want to sketch the infuence ine for any force quantity (ike thrust, shear, reaction, support moment or bending moment) in a structure, (i) We remove from the structure the resistant to that force quantity and (ii) We appy on the remaining structure a unit dispacement corresponding to that force quantity. The resuting dispacements in the structure are the infuence ine ordinates sought. 14. State Maxwe-Betti s theorem. 1 A B C R A R B R C In a ineary eastic structure in static equiibrium acted upon by either of two systems of externa forces, the virtua work done by the first system of forces in undergoing the dispacements caused by the second system of forces is equa to the virtua work done by the second system of forces in undergoing the dispacements caused by the first system of forces. 15. What is the necessity of mode anaysis? (i) (ii) (iii) When the mathematica anaysis of probem is virtuay impossibe. Mathematica anaysis though possibe is so compicatedand time consuming that the mode anaysis offers a short cut. The importance of the probem is such that verification of mathematica anaysis by an actua test is essentia. 16. Define simiitude. Simiitude means simiarity between two objects namey the mode and the prototype with regard to their physica characteristics: Geometric simiitude is simiarity of form Kinematic simiitude is simiarity of motion Dynamic and/or mechanica simiitude is simiarity of masses and/or forces.
17. State the principe on which indirect mode anaysis is based. The indirect mode anaysis is based on the Muer Bresau principe. Muer Bresau principe has ead to a simpe method of using modes of structures to get the infuence ines for force quantities ike bending moments, support moments, reactions, interna shears, thrusts, etc. To get the infuence ine for any force quantity, (i) remove the resistant due to the force, (ii) appy a unit dispacement in the direction of the (iii) pot the resuting dispacement diagram. This diagram is the infuence ine for the force. 18. What is the principe of dimensiona simiarity? Dimensiona simiarity means geometric simiarity of form. This means that a homoogous dimensions of prototype and mode must be in some constant ratio. 19. What is Begg s deformeter? Begg s deformeter is a device to carry out indirect mode anaysis on structures. It has the faciity to appy dispacement corresponding to moment, shear or thrust at any desired point in the mode. In addition, it provides faciity to measure accuratey the consequent dispacements a over the mode. 20. Name any four mode making materias. Perspex, pexigass, acryic, pywood, sheet aradite and bakeite are some of the mode making materias. Micro-concrete, mortar and paster of paris can aso be used for modes. 21. What is dummy ength in modes tested with Begg s deformeter. Dummy ength is the additiona ength (of about 10 to 12mm) eft at the extremities of the mode to enabe any desired connection to be made with the gauges. 22. What are the three types of connections possibe with the mode used with Begg s deformeter. (i) Hinged connection (ii) Fixed connection (iii) Foating connection 23. What is the use of a micrometer microscope in mode anaysis with Begg s deformeter. Micrometer microscope is an instrument used to measure the dispacements of any point in the x and y directions of a mode during tests with Begg s deformeter.
PART B 1. A beam ABC is supported at A, B and C as shown in Fig. 7. It has the hinge at D. Draw the infuence ines 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 infuence ine ordinates at any section X on BC of the continuous beam ABC shown in Fig. 8, for reaction at A. X x A B C 5m 5m 3. In Fig. 1, D is the mid point of AB. If a point oad W traves from A to C aong the span where and what wi be the maximum negative bending moment in AC. A Ä D B ÄBF C Fig. 1. 4. Sketch quaitativey the infuence ine for shear at D for the beam in Fig. 2. (Your sketch sha ceary distinguish between straight ines and curved ines) A Ä B DAI Ä D CAK Ä C 5. A singe roing oad of 100 kn moves on a girder of span 20m. (a) Construct the infuence ines for (i) Shear force and (ii) Bending moment for a section 5m from the eft support. (b) Construct the infuence ines for points at which the maximum shears and maximum bending moment deveop. Determine these maximum vaues.
6. Derive the infuence diagram for reactions and bending moment at any section of a simpy supported beam. Using the ILD, determine the support reactions and find bending moment at 2m, 4m and 6m for a simpy supported beam of span 8m subjected to three point oads of 10kN, 15kN and 5kN paced at 1m, 4.5m and 6.5m respectivey. 7. Two concentrated roing oads of 12 kn and 6 kn paced 4.5 m apart, trave aong a freey supported girder of 16m span. Draw the diagrams for maximum positive shear force, maximum negative shear force and maximum bending moment. 8. Determine the infuence ine for R A for the continuous beam shown in the fig.1. Compute infuence ine ordinates at 1m intervas. Anayse the continuous beam shown in figure by sope defection method and draw BMD. EI is constant.
UNIT-III ARCHES 1.What is an arch? Expain. An arch is defined as a curved girder, having convexity upwards and supported at its ends. The supports must effectivey arrest dispacements in the vertica and horizonta directions. Ony then there wi be arch action. 2.What is a inear arch? If an arch is to take oads, say W 1, W 2, and W 3 (fig) and a Vector diagram and funicuar poygon are potted as shown, the funicuar poygon is known as the inear arch or theoretica arch. p W2 q Q R W 1 W 2 W 3 PQ R S O t P C O E S W1 D W 3 r A T B Space Diagram H Vector Diagram s The poar distance ot represents the horizonta thrust. The inks AC, CD, DE, and EB wi be under compression and there wi be no bending moment. If an arch of this shape ACDEB is provided, there wi be no bending moment. For a given set of vertica oads W 1, W 2..etc., we can have any number of inear arches depending on where we choose O or how much horizonta thrust (ot) we choose to introduce. 3.State Eddy s theorem. Eddy s theorem states that The bending moment at any section of an arch is proportiona to the vertica intercept between the inear arch (or theoretica arch) and the centre ine of the actua arch. BM x = Ordinate O 2 O 3 x scae factor X W2 W 1 W 3 o 2 o 3 Actua arch Theoretica arch x o 1
X 4.Expain with the aid of a sketch, the norma thrust and radia shear in an arch rib. H A B H N R Let us take a section X of an arch. (fig (a) ). Let θ be the incination of the tangent at X. If H is the horizonta thrust and V the vertica shear at X, from the free body of the RHS of the arch, it is cear that V and H wi have norma and radia components given by, N= H cosθ + Vsinθ R= V cosθ -Hsinθ 5. Which of the two arches, viz. circuar and paraboic is preferabe to carry a uniformy distribute oad? Why? Paraboic arches are preferaby to carry distributed oads. Because, both, the shape of the arch and the shape of the bending moment diagram are paraboic. Hence the intercept between the theoretica arch andactua arch is zero everywhere. Hence, the bending moment at every section of the arch wi be zero. The arch wi be under pure compression which wi be economica. 6.What is the difference between the basic action of an arch and a suspension cabe? An arch is essentiay a compression member which can aso take bending moments and shears. Bending moments and shears wi be absent if the arch is paraboic and the oading uniformy distributed. A cabe can take ony tension. A suspension bridge wi therefore have a cabe and a stiffening girder. The girder wi take the bending moment and shears in the bridge and the cabe, ony tension.because of the thrusts in the cabes and arches, the bending moments are consideraby reduced. If the oad on the girder is uniform, the bridge wi have ony cabe tension and no bending moment on the girder. 8.Under what conditions wi bending moment in an archbezerothroughout. The bending moment in an arch throughout the span wi be zero, if (i) the arch is paraboic and (ii) the arch carries uniformy distributed oad throughout the span. 9.Draw the ILD for bending moment at a section X at a distance x from the eft end of a three hinged paraboic arch of span and rise h. M x = x Hy x Hy
(+) (-) x(-x)/ x(-x)/ 10. Indicate the positions of a moving point oad for maximum negative and positive bending moments in a three hinged arch.
Considering a three hinged paraboic arch of span and subjected to a moving point oad W, the position of the point oad for a. Maximum negative bending moment is 0.25 from end supports. b. Maximum positive bending moment is 0.211 from end supports. 11. Draw the infuence ine for radia shear at a section of a three hinged arch. Radia shear is given by F x = H sinθ - V cosθ, where θ is the incination of tangent at X. sinθ x cosθ 4r x cosθ 12. Sketch the ILD for the norma thrust at a section X of a symmetric three hinged paraboic arch. Norma thrust at X is given by P = H cosθ + V sinθ, where θ is the incination of tangent at X. x sinθ (-x)sinθ 4y c cosθ 13. Distinguish between two hinged and three hinged arches. S.No. Two hinged arches Three hinged arches 1. Staticay indeterminate to first degree Staticay determinate 2. Might deveop temperature stresses Increase in temperature causes increase in centra rise. No stresses. 3. Structuray more efficient Easy to anayse. But in costruction, the centra hinge may invove additiona expenditure. 4. Wi deveop stresses due to sinking of Since this is determinate, no stresses due to supports support sinking.
14. Expain rib-shortening in the case of arches. In a two hinged arch, the norma thrust which is a compressive force aong the axis of the arch wi shorten the rib of the arch. This in turn wi reease part of the horizonta thrust. Normay, this effect is not considered in the anaysis (in the case of two hinged arches). Depending upon the importance of the work we can either take into account or omit the effect of rib shortening. This wi be done by considering (or omitting) strain energy due to axia compression aong with the strain energy due to bending in evauating H.
15. Expain the effect of yieding of support in the case of an arch. Yieding of supports has no effect in the case of a 3 hinged arch which is determinate. These dispacements must be taken into account when we anayse 2 hinged or fixed arches under U = H instead of zero H U = V A instead of zero V A Here U is the strain energy of the arch and H and V A are the dispacements due to yieding of supports. 16. Write the formua to cacuate the change in rise in three hinged arch if there is a rise in temperature. Change in rise = 2 + 4r 2 4r α T where = span ength of the arch r = centra rise of the arch α = coefficient of therma expansion T = change in temperature 17. In a paraboic arch with two hinges how wi you cacuate the sope of the arch at any point. Sope of paraboic arch = θ = tan -1 4r ( 2x) 2 where θ = Sope at any point x (or) incination of tangent at x. = span ength of the arch r = centra rise of the arch 19. How wi you cacuate the horizonta thrust in a two hinged paraboic arch if there is a rise in temperature. α TEI Horizonta thrust = y 2 dx 0 where = span ength of the arch y = rise of the arch at any point x α = coefficient of therma expansion T = change in temperature E = Young s Moduus of the materia of the arch I = Moment of inertia 19. What are the types of arches according to the support conditions. i. Three hinged arch ii. Two hinged arch
iii. Singe hinged arch iv. Fixed arch (or) hingeess arch 20. What are the types of arches according to their shapes. i. Curved arch ii. Paraboic arch iii. Eiptica arch iv. Poygona arch
UNIT-1V SLOPE-DEFLECTION METHOD 1.What are the assumptions made in sope-defection method? (i) Between each pair of the supports the beam section is constant. (ii) The joint in structure may rotate or defect as a whoe, but the anges between the members meeting at that joint remain the same. 2. How many sope defection equations are avaiabe for a two span continuous beam? There wi be 4 nos. of sope-defection equations, two for each span. 3. What is the moment at a hinged end of a simpe beam? Moment at the hinged ends of a simpe beam is zero. 4. What are the quantities in terms of which the unknown moments are expressed in sopedefection method? In sope-defection method, unknown moments are expressed in terms of (i) sopes (θ) and (ii) defections ( ) 5. The beam shown in Fig. is to be anaysed by sope-defection method. What are the unknowns and, to determine them, what are the conditions used? A B C Unknowns: θ A, θ B, θ C Equiibrium equations used: (i) M AB = 0 (ii) M BA + M BC = 0 (iii) M CB = 0 6. How do you account for sway in sope defection method for porta frames? Because of sway, there wi br rotations in the vertica members of a frame. This causes moments in the vertica members. To account for this, besides the equiibrium, one more equation namey shear equation connecting the joint-moments is used. 7. Write down the equation for sway correction for the porta frame shown in Fig. The shear equation (sway correction) is MAB + MBA MCD + + MDC = 0 A D 8. Write down the sope defection equation for a fixed end support. A B C D The sope defection equation for end A is M AB = M AB + 2EI θ A + θ B + 3
Here θ A = 0. Since there is no support settement, = 0. MAB = M AB + 2EI B + 3
9. Write down the equiibrium equations for the frame shown in Fig. B C Unknowns : θ B, θ C Equiibrium equations : At B, M BA + M BC = 0 h At C, M CB + M CD = 0 M AB + M BA Ph + M CD + M DC + P P Shear equation : = 0 A D 10. Who introduced sope-defection method of anaysis? Sope-defection method was introduced by Prof. George A.Maney in 1915. 11. Write down the genera sope-defection equations and state what each term represents? A B Genera sope-defection equations: MA B = M AB + 2EI θ A + θ B + 3 MB A = M BA + 2EI θ B + θ A + 3 where, M AB, M BA = Fixed end moment at A and B respectivey due to the given oading. θ A, θ B = Sopes at A and B respectivey = Sinking of support A with respect to B 13. Mention any three reasons due to which sway may occur in porta frames. Sway in porta frames may occur due to (i) unsymmetry in geometry of the frame (ii) unsymmetry in oading or (iii) Settement of one end of a frame. 13. How many sope-defection equations are avaiabe for each span? Two numbers of sope-defection equations are avaiabe for each span, describing the moment at each end of the span. 14. Write the fixed end moments for a beam carrying a centra cockwise moment. A B /2 /2 Fixed end moments : M AB = M BA = M 4
15. State the imitations of sope defection method. (i) It is not easy to account for varying member sections (ii) It becomes very cumbersome when the unknown dispacements are arge in number. 16. Why is sope-defection method caed a dispacement method?