BRANCH : CIVIL ENGINEERING DISPLAY DATE : BATCH ...€¦ · 2 Darshan Institute of Engineering & Technology 2150608 - S.A. – II (ASSIGNMENT) DEPARTMENT OF CIVIL ENGINEERING 1. Using

1 Darshan Institute of Engineering & Technology

2150608 - S.A. – II (ASSIGNMENT)

DEPARTMENT OF CIVIL ENGINEERING

1. Find the displacement at C, as shown in fig. (i) By using Castigliano’s theorem. E = 2 X 104N/mm2

2. Determine the vertical deflection at free end in the overhanging beam as Shown in fig. (ii). Assume constant EI. Use Castigliano’s method.

3. Find the displacement of B, for fig. (iii), by Castigliano’s theorem. Sectional area varies linearly from A to B.

4. For continuous beam ABC as shown in fig. (iv), determine support reactions with the use of Castigliano’s theorem.

5. Calculate fixed end moments for a beam as shown in fig. (v) Using Castigliano’s theorem. Draw shear force diagram and bending moment diagram.

6. Determine the deflection at point C of an overhanging beam as shown in fig. (vi). Adopt E = 2 x 105 N/mm2 and I = 2 x 108 mm4

7. Determine horizontal deflection at point D for the frame as shown in fig. (vii). Adopt I = 2 x 108 mm4 and E = 2 x 105 MPa.

8. Determine the vertical deflection of joint C of the truss shown in fig. (viii). by unit load method. The cross-sectional area of each member is 400 mm2. E = 2 × 105 N/mm2.

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Chapter-1 Energy Principles




1. Using slope deflection method analyses the beam as shown in fig. (i). Draw SFD and BMD

both. 2. Analyse the beam shown in fig. (ii) by slope deflection method and find unknown slopes at

Joint B and C. Joint B sinks by 10 mm. E = 2 × 105 MPa and I = 16 × 107 mm4. 3. Find the final moments at supports for the beam shown in fig. (ii) and plot SF and BM

diagram both. 4. Determine the support moments using slope deflection method for the continuous girder

shown in fig. (iii), if the support B sinks by 2.5 mm. For all members Take E = 200 kN/mm2 and I = 3.5 × 107 mm4.

5. Determine the support moments using slope deflection method for the frame as shown in fig. (iv). Also draw Bending Moment diagram.

6. A beam AB of uniform section of span 9m and constant EI=3.6x104 Nm2 is partially fixed at ends when the beam carries a point load of 90 kN at distance of 3m from the left end A. The following displacements were observed. (i) rotation at A = 0.01 rad (clockwise) and settlement at A= 20 mm (ii) rotation at B = 0.0075 rad (anticlockwise) and settlement at B= 15 mm

Analyse using Slope Deflection Method. 7. Using slope deflection method analyse the continuous beam shown in fig. (v).Draw bending

moment diagram. 8. Analyse the continuous beam shown in fig. (vi).by slope deflection method. Draw shear

force diagram and bending moment diagram.

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Chapter-2 Slope deflection method




1. Determine the support moment for a continuous beam as shown in fig. (i). by moment distribution method. Also draw bending moment diagram.

2. For a continuous beam ABCD as shown in fig. (ii). find the moments at all supports if, end A rotates by 0.002 radian in the clockwise order and the support B settles by 4 mm. E = 200 x103 N/mm2 and I = 9 x 107 mm4.

3. Determine the support moments using moment distribution method for the frame as shown in fig. (iii). Also draw Bending Moment diagram.

4. Analyse the Portal frame shown in fig. (iv). By Moment Distribution Method and draw B.M. Diagram and S.F. Diagram.

5. Define the term ‘sway’. Enlist the situation wherein say occur in portal frames. 6. Analyse the portal frame shown in fig. (v). by moment distribution method and find only

final moments. 7. Determine the support moments and draw BMD for the beam shown in fig. (vi) by

Moment Distribution Method. 8. Determine end moments for frame loaded as shown in fig. (vii) using moment

distribution method. Take EI = constant for all members.

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Chapter-3 Moment distribution method


2150608-S.A.-II (Assignments)


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QUESTIONS

1 State the Importance of the Influence Lines. Give the Difference between Influence Line Diagram and

SF & BM Diagrams.

2 A simply supported beam AB has a span of 8m.Draw influence lines for RA, RB,VX & MX for a section

3m from left end support.

3 A train of loads as shown in figure.1 crosses a simply supported girder of span18m from left to right.

Calculate maximum SF& BM at section 8m from left.

4 A simple support beam has span of 20m and loaded by a train of wheels as shown in the figure.2.

Calculate the maximum bending moment and shear force induced at 8m from left support.

5 Draw the influence line diagram for the beam shown in figure.3 (i) the reaction at A (ii) the reaction at

C(iii) the shear at B.

6 Two wheel loads of 16 kN& 8 kN, at a fixed distance apart of 2 m, cross a beam of 10m span. Draw the

influence line for B.M & S.F for a point 4m from the left abutment & find the maximum B.M & S.F at

that point.

7 A simple support beam of span 30 m is loaded by a train of six wheel loads each of equal magnitude 5

kN and separated by 2 m distance. Calculate the maximum positive and negative shear force and

bending moment at 10m from left support.

8 A uniformly distributed load of 12 kN/m and 3 m length crosses a simply supported girder of span 10m

from left to right. Draw influence line for shear force and bending moment at 4m from left hand and

find maximum shear force and bending moment at this section. Refer figure.4.

9 Five wheel loads as shown in figure.5, crosses a simply supported beam of span 24 m from left to right.

Calculate the maximum positive and negative SF at the centre of the span and absolute maximum BM

anywhere in the span. (14 Marks)

10 Draw IL diagram for forces in the members U2U3, L1L2, U3L3, U2L3 & L1U2 of a Pratt Truss as shown in

figure.6.



Chapter-4 Assignment-4 Influence Lines for Determinate Structure




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SN QUESTIONS

1 Explain the Muller Breslau’s principle. How it will be useful for the indeterminate

beam?

2 Compute the ordinates of ILD for reaction at A for the figure.1.

3 For a two span simple support continuous beam ABC having AB=4m and BC=5m,

calculate the ILD ordinates for RA at every 1m interval.

4 For a two span simple support continuous beam ABC having AB=4m and BC=5m,

calculate the ILD ordinates for RA at every 1m interval.

5 Generate the influence line diagram for MA and RB. Refer figure.2.

6 Plot influence line for vertical reaction at support A for the two span continuous beam

shown in figure.3. Compute ordinate at every 1 m interval. Also plot qualitative ILD for

reaction at B and C.

7 Draw the influence lines for (i) reaction at B, (ii) and moment at A for the beam as

shown in figure.4. Compute the ordinates at intervals of 2.0 meter.

8 Draw influence line diagrams of reaction at A and B for a propped cantilever beam AB

of span 5 m with ordinate interval of 1.0 m using Muller Breslau principle.

9 Draw influence line diagrams of reaction at B (RB) and reaction at C (RC) for a

continuous beam ABC with both span length of 8 m having interval of 2 m using Muller

Breslau principle.

10 Draw the ILD for moment at B in the continuous beam as shown in figure.5. Calculate

the ordinates at 2 m intervals, assuming EI is constant throughout.

11 Draw the ILD for shear force at D in the continuous beam as shown in figure.6.

Calculate the ordinates at 1 m intervals, assuming EI is constant throughout.



Chapter-5 Assignment-5 Influence Lines for Indeterminate Structure




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SN QUESTIONS

1 Differentiate between stiffness method and flexibility method.

2 For the structure shown in the figure.1 calculate the stiffness matrix and load vector.

3 For the above problem Q.2, calculate the nodal displacements and hence draw the

shear force and bending moment diagrams.

4 For the structure shown in the figure.2 calculate the stiffness matrix and load vector.

5 For the above problem Q.4, calculate the nodal displacements and hence draw the

shear force and bending moment diagrams.

6 Develop stiffness matrix for the plane frame shown in figure.3 Neglect axial

deformations.

7 Analyse the beam shown in figure.4, by stiffness method.

8 Formulate the Stiffness matrix [S] and load vector {AD – ADL} for the beam shown in

figure 5.

9 For the beam shown in figure 5, calculate joint displacements and final end moments

using stiffness method. Also draw SF and BM diagrams

10 Find the rotations at supports ‘B’ and ‘C’ of a 2 span continuous beam ABC of

constant flexural rigidity ‘EI’ carrying a clockwise moment of magnitude 12 kN-m at ‘B’.

Supports ‘B’ & ‘C’ are simple supports and ‘A’ is a fixed support. Spans AB and BC

are 4 m long. Use stiffness method.



Chapter-6 Assignment-6 Matrix Methods (Stiffness Method)




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SN QUESTIONS

1 For the structure shown in the figure.1 calculate the flexibility matrix and displacement vector. Assume all the reaction at support B, C and D as unknown forces.

2 For the above problem Q.1, calculate the values of all the unknown reactions and draw the shear force and bending moment diagrams.

3 Analyze the beam shown in figure.2, by flexibility method. If support A and C are replaced by hinge supports.

4 Develop flexibility matrix for the plane frame shown in figure.3. 5 Formulate the Flexibility matrix [F] and vector {DQL} for the beam shown in figure.4.

Assume MA and MB as redundant. 6 For the beam shown in figure.4, calculate values of all unknown reactions using

Flexibility method. Also draw SF and BM diagram. 7 A truss is made up of 6 members AB, BC, CD, DA, AC and BD of equal axial rigidity.

Co-ordinates of joints are A(0,3), B(3,3), C(3,0) & D(0,0). It carries a vertical downward load of magnitude 24kN at joint ‘B’. Support ‘D’ is hinged. ‘C’ is roller support offering a vertical reaction. Find the redundant force in member ‘AB’ using flexibility method.

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Chapter-6 Assignment-6 Matrix Methods (Stiffness Method)

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BRANCH : CIVIL ENGINEERING DISPLAY DATE : BATCH ...€¦ · 2 Darshan Institute of Engineering & Technology 2150608 - S.A. – II (ASSIGNMENT) DEPARTMENT OF CIVIL ENGINEERING 1. Using