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Candidates are required to give their answers in their own words as far as practicable.

All questions carry equal marks.

Attempt any FOUR questions selecting at lest ONE question from each GROUP.

GROUP‐A Q. [1] Analyze by Force Method, the Rigid Frame with

two hinged support at the base is loaded as shown in Fig. [1]. Find the Reaction a supports and draw Bending Moment diagram.

Q. [2] Using moment distribution method, analyze the

frame shown in Fig[2]. Draw B.M.D.

Q. [3] Analyze A continuous Beam ABCD by Slope‐

Deilectic method. Find the Bending Moment at ABCD, if support rotates by 0.002 radian in the clockwise order and the support B sinks by 4 millimeters. Draw bending moment diagram. E= 200KN/mm2 I=9*107 mm4

Q. [4] Using the Displacement (stiffness Matrix) Method, analyze and determine the Bending Moment at each support and draw moment diagram of the continuous Beam shown in Fig. [4]. All members have the same‐ flexural rigidity.

PURWANCHAL UNIVERSITYV SEMESTER FINAL EXAMINATION‐2003

LEVEL : B. E. (Civil)

SUBJECT: BEG357CI, Theroy of Structure‐II. Full Marks: 80TIME: 03:00 hrs Pass marks: 32



Q. [5] [a] A two hinged parabolic arch of span 40 meter and rise 8 meter is subjected to u.d.l as shown in Fig. 5[b]. Find the horizontal thrust and maximum bending stress at the crown due to load. The rib section is 1000 millimeter V and 300 mm wide. E=2*105 N/mm2. Neglect effect of rib shortening

[b] Determine and draw the influence line for the

bending moment at support B of a continuous beam shown in Fig. 5[b], Compute the ordinates at meter interval.

Q. [6] [a] Find out the reaction forces, using Castiglianoʹs

second theory (∆=θU/θP=0) of the Structure shown in Fig. 6[a]. Draw bending moment diagram.

[b] A Rectangular portal frame whose legs are fix the base. The frame carries a point load 2W at mid span and a horizontal sideway load W/2. Find the value of W at which the frame collapse. All members are of same section.

uz

Fig. 6fo1




All questions carry equal marks. The marks allotted for each sub‐question is specified along its side.


GROUP‐A Q. [1] [a] Compute the bar forces due to applied load as

shown in Fig. [1] and an increase of temperature of 40°C in the temperature at bars AE and FD. No change in the temperature of any other bars, αt =12*106/°C. Cross sectional areas for all members=4cm2. [20]

Q. [2] [a] Explain the equation of compatibility. [6]

[b] Using the method of slope deflection analyse the continuous beam shown in Fig. 2 [b] due to the settlement of 4mm at support B. Draw S.F.D. and B.M.D. Sketch the elastic curve. Take E=4xl04 N/mm2, I=4000 cm2. [14]

Q. [3] Analyze the rigid frame shown in Fig. [3] by

moment distribution method. Draw shear and moment diagrams. [20]

GOURP‐B Q. [4] [a] Derive the slope deflection equations. [6] [b] Analyze the frame shown in Fig. 4 [b] by

flexibility or stiffness matrix method. [14]



SUBJECT: BEG357CI, Theory of Structure‐II. Full Marks: 80TIME: 03:00 hrs Pass marks: 32

Fig 2



Q. [5] [a] A two hinged parabolic arch of span 40 m and 5m

central rise is hinged at supports. It carries a concentrated load of l00kN at a distance of 10 meters from the left support. Calculate the horizontal thrust and also bending moment, normal thrust under the load.

Take I= Ic secθ where θ is the inclination of the parabolic arch at the section to the horizontal and Ic is the moment of inertia of the section at the crown. [8]

[b] Draw the influence line for bending moment at the intermediate support B of the continuous beam ABC of the uniform moment of inertia. [12]

Q. [6] [a] Calculate the change in slope at support C using Castiglianoʹs theorem. [6]

[b] Determine the plastic moment capacity of the

beam for the beam shown in Fig. 6 [b]. [14]



Candidates are required to give their answers in their own words as ]far as practicable.

All questions carry equal marks. The marks allotted for each sub‐question is specified along its side.


GROUP‐A Q. [1] Find the forces in the various member of truss

given in Fig. [1] by using force method. The cross section area of each member is 500mm2. The truss is pinned at A and rests on roller at D. [Take member BE as redundant]. [20]

Q‐ [2] [a] Define the term plastic hinge, plastic moment and……………

[b] Analyze and draw bending moment diagram of the beam shown in Fig. [2] by using slope

Deflection method. What are the reaction at supports? [14]

Q. [3] A portal frame shown in Fig. [3] is to resist a

horizontal load of 5KN applied at B. The moment of inertia of the column section is I and moment of inertia of beam is 2I. Determine the bending moment developed at B and C and sketch the bending moment diagram for entire span.

GROUP‐B

PURWANCHAL UNIVERSITYV SEMESTER BACK‐PAPER EXAMINATION‐2004





Q. [4] [a] What do you understand by the term ʹDistribution factorʹ? Discuss its importance in the method of moment distribution. [6]

[b] Analyze for end moments of the given frame by using matrix method. Draw bending moment diagram. EI is constant for all members. The frame is fixed at A and pinned at C. [14]

Q. [5] [a] Determine all induced reaction due to a vertical

settlement of 3mm at the support B of the given beam by using force method. Take EI=32000 KN‐m2 Fig. 5[a]. The beam is pinned at A and B and fixed at C. [8]

[b] Determine the influence line for reaction at B for propped cantilever beam. Compute the ordinates at every 1.25 meter interval Fig. 5[bJ. [12]

Q. [6] [a] Prove that the castigliano theorem ∆i= dU/dPi [6] Where ∆i ‐ Deflection at point. dU/dPi — Partial derivative of total energy in

beam with respect to load applied at any point. [b] A beam of rectangular cross‐section B×D is

subjected to a bending moment 0.7Mp. Find out the depth of the elastic core. [14]

Fig.




Full marks are given in parenthesis.

Attempt any FOUR questions. Q. [1] Using Consistent Deformation Method; find and

draw the S.F., B.M. and Axial force diagram of frame loaded as shown in fig.[1] [20]

Q. [2] [a] What is shape factor explain briefly and find the

shape of factor of circular section with diameter D. [6]

[b] If support B sinks 8.15 mm, determine the moment at joint using slope deflection method. Take EI constant. [14]

Q. [3] Explain moment distribution method. Analyze the

frame using moment distribution method. Draw D.M.D. [20]

Q. [4] [a] Explain effect of sinking of support. Find the

fixed‐end moment in this case. [6] [b] Analyze the frame using matrix method. [14] Q. [5] [a] Find‐the reactions of two hinged arch loaded as

shown in fig.5[a] [8]






[b] Draw the influence line diagram for BM of the

mid span of beam AB. [12] Q. [6] [a] Find the BM at support A of beam as shown in

fig. by using Castiglianoʹs theorem. [6] [b] Find the shape factor of T section as shown in fig.

Take σy =240N/mm2. [14]





Attempt any FOUR questions. Q. [1] Figure shows four steel rod OA, OB, OC and OD

having same cross sectional area laying in the same vertical plane supporting a load of 40 KN at O. Determine the forces developed in each of the rod if the member OA goes up by 20Co. Take coefficient of linear expansion α = 12 x l0‐6 /0C. Fig.[l]. [20]

Q. [2] Analyze the loaded frame by using Slope Deflection Method. Draw Bending moment diagram and elastic curve. [20]

Q. [3] Using matrix method, analyze the end moment of

the given frame. Draw bending moment diagram. [20] Q. [4] Determine the support moment for the given

structure by using moment distribution method. Draw bending moment diagram. El constant. [20]






Q. [5] [a] Determine the reaction components, and draw

bending moment diagram of given beam by using force method. EI constant. [8]

[b] Using muller‐Breslau principle. Draw the

influence line diagram for reaction at C(Rc) of given beam after computing the values of the ordinates at 2 meter interval. [12]

Q. [6] [a] In the continuous shown in Fig.6.[a], plastic moment capacity of AB is kept three times that of BC. Determine plastic moment capacity of the beam if the loads shown are working load. Take load factor=l .2. [12]

[b] Determine the reaction forces at supports and

draw bending moment diagram by using principle of least work. EI constant. [8]

Fig. 6 [b]





Attempt any FOUR question at least ONE questions from each group.

GORUP‐A Q. [1] Figure shows four steel rod OA, OB, OC and OD

having same cross sectional area laying in the same vertical plane supporting a load of 40 KN at O. Determine the forces developed in each of the rod if the member OA goes up by 20Co. Take coefficient of linear expansion α = 12 x l0‐6 /0C. Fig.[l]. [20]

Q. [1] Analyse the given truss by Force method and determine the actual forces in the members if the member BD goes up by 15 ° C, Sectional area of each member is 200 mm2 .E= 200KN/ mm2 . Take Coefficient of linear expansion a = 12*10”6/°C Fig.[l]. [20]

Q. [2] Analyze the loaded frame by using Slope Deflection Method, If the support B sink by 3 mm. Draw Bending moment diagram and elastic curve. Take E=200KN/mm2 and I = 3.5*107mm4 [Fig.2] [20]

Q. [3] Using matrix method, analyze the end moment of

the given beam. Draw bending moment diagram. [Fig.3] [20]

GOURP‐B






Q. [4] [a] Determine the support moment for the given structure by using moment distribution method. Draw bending moment diagram. EI constant [Fig. 4]. [20]

Q. [5] [a] Using muller‐Breslau principle. Draw the

influence line diagram for reaction at B (RB) of given beam after computing the values of the ordinates at 2 meter interval. [Fig. 5 a] [12]

[b] Determine the reaction components and draw

bending moment diagram of given beam by using force method. El constant. [Fig. 5 b] [8]

Q. [6] [a] Collapse loads acting on the frame are shown in

figure. Determine the plastic moment capacity of the section required. [12]

Q‐ [6] [b] Determine the reaction forces at supports and

draw bending moment diagram by using principle of least work. El constant [Fig. 6 b] [8]

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Downloaded from · PDF fileQ. [2] Using ... Determine and draw the influence line for the ... SUBJECT: BEG357CI, Theory of Structure‐II