GOVERNMENT ENGINEERING COLLEGE DAHOD APPLIED …GOVERNMENT ENGINEERING COLLEGE DAHOD Applied...

GOVERNMENT ENGINEERING COLLEGE DAHOD

APPLIED MECHANICS DEPARTMENT

B.E. II (CIVIL) (FOURTH SEMESTER)

2018-2019

SUBJECT: STRCTURAL ANALYSIS - I

Subject code: 2140603

Name of student:

Enrollment no:

Faculty conveyer,

1. Prof. B. M. Purohit

2. Prof Y K Tandel

3. Prof. N. B. Umravia

4. Prof M. A. Shaikh

5. Prof R. A. Jhumarwalla


Applied Mechanics department

April- 2019

CERTIFICATE

This is to certify that the Mr /Miss_____________________________

_____________________________________ of BE – II year 4th

Semester

class Enrollment No ______________________ and Exam No

__________________

Has satisfactorily completed his / her Term work in “Structural

Analysis- I 2140603) for the term ending in April 2019

Date:_______________

Sign of Teacher

Head of the Department


APPLIED MECHANICS DEPARTMENT

2018- 2019

NAME :_______________________________________________________

Roll No :__________________ Enroll No: ___________________

YEAR: - BE I (4th

Semester) Civil

Subject: “Structural Analysis - I” (2140603)

SR.

NO

COURSE CONTENT Page DATE GRADE SIGN REMARK

1. Tutorial -1

Fundamentals of Statically

Determinate Structures:

2. Tutorial -2

Displacement of Determinate

Beams and Plane Truss:

3. Tutorial -3

Direct and Bending stresses:

4. Tutorial -4

Columns and Struts:

5. Tutorial -5

Arches, Cables and Suspension

Bridges:

6. Tutorial -6 Thin cylinder:

7. Tutorial -7

Fixed Beams & Consistent

Deformation Method:

8. Tutorial -8

Strain Energy


Tutorial – 1 FUNDAMENTALS OF STATICS

1. Define statically determinate and indeterminate structures.

2. Distinguish between statically determinate and indeterminacy of the structures

3. Explain „degree of static indeterminacy‟.

4. Explain maxwell‟s theorem of reciprocal deflection.

5. Defined „kinematics indeterminacy of a structure‟ Explain with sketches.

6. State and Explain Principle of Superposition with suitable example.

7. Define statically determinate and indeterminate structures.

8. Differentiate between the terms: BEAM, TRUSS, FRAME and ARCH.

9. “Indeterminate structures are better than determinate structures” Comment on the

statement.

10. Find static indeterminacy and kinematic indeterminacy of structures given in below

figure.

11. Explain and prove Maxwell‟s reciprocal theorem with example.

12. Find SI and KI for the structures shown in fig.1 to 20.

Fig. 1 Fig. 2

Internal hinge

Fig. 3 Fig. 4

Internal hinge A

B C D

E

Fig. 5

A B

C D

Fig. 6

A B C D

Fig. 7

A B C

D

E Internal hinge


Fig. 8

Internal hinge

Fig. 9

Fig. 10

Fig. 11

Fig. 13 Fig. 14 Fig. 15 Fig. 16

Fig. 17 Fig. 18 Fig. 19


TUTORIAL-2

DISPLACEMENT OF DETERMINATE BEAMS & PLANE TRUSS

1. Relation between slope deflection and radius of curvature.

2. Defined Macauli‟s method.

3. A horizontal steel girder having uniform cross-section is 14 m long and is simply

supported at its ends. It carries two concentrated loads as shown in fig. Find deflection

of beam at A and B by Macauli‟s method.

4. A beam of length 8 m is simply supported at its ends. It carries a uniformly distributed

load of 40 kN/m as shown in fig. determine the deflection of the beam at its mid- point

and also the portion of maximum deflection and maximum deflection by Macauli‟s

method Take E= 2 x 105 N/ mm

2 and I = 4.3 x 10

6 mm

4.

5. A beam ABC of length 9 m has one support of left end and the other support at a

distance of 6 m from left end. The beam carries a point load of 1 kN at right end and

also carries a uniformly distributed load of 4 kN/m over a length a length of 3 m as

shown in fig. determine the slope and deflection at point C. Macauli‟s method take E =

2 x 105N/mm

2 and I = 5 x 10

8 mm

4.

6. Determine the rotation at A and deflection under concentrated load at mid span in the

beam shown in fig. by moment area method.

A

6m 3 m

4 kN/m

3m

C

12kN

D B

A

C D

B

40 kN/m

4m 3m 1m

20 kN 20 kN

A

C D

B

I

2I

I 3m 4m 2m

8 kN

12 kN

14 m

C

A B D

6.5 m 4.5 m 3 m


7. Determine the rotation and deflection at B and C in the cantilever beam shown in fig.

by moment area method.

8. Determine slope and deflections at the end of the beam shown in fig. EI is constant

throughout by, Moment area method.

9. Determine the rotations at A, B, C, D and deflection at C, D and E in the beam shown

in fig. by Conjugate beam method.

10. Determine the rotation and deflection at the free end in the overhanging beam as

shown in fig. by Conjugate beam method.

11.Using conjugate beam method, determine the deflection and rotation at the free end in

the beam as shown in fig. by Conjugate beam method.

12. As shown in Fig. represents a Crane structure attached to a vertical wall and carrying

a vertical load of 20 kN at C. all tension members are stressed 80 N/mm2 and all

compression members to 50 N/mm2.determine horizontal and vertical deflection of the

end C. Take E = 2 x 105 N/mm

2 all members, except CD, have a length of 2 m AE = 2

m.

L/

2

W/ unit length

A C B

L/2 L/2

80 kN 25 kN

2 m 2 m 2 m

A

B C D

2 m

m 2 m

m 2 m

m

60 kN

I 2I I

2 m 2 m 2 m 2 m A B D C E 2 m 2 m 2 m 2 m

L/3

D

A C

W/ unit length

B

L L/3

20 kN/ m 10 kN

2I I

B A

1 m 1 m


13. Fig. shows the outline of truss used for lifting a load which is distributed as 2 kN on

each of the four points Q, R, S and T. the members PQ, PR, PS and PT each have an

area of the 65 Sq. mm and members QR, RS and ST each have of 130 Sq. mm.

Determine vertical deflection of Q and R relative to support P.

14. The members of the warren girder shown in fig. are so proportioned that all the

members are stressed to 100 N/mm2. When a vertical load of 60kN is applied at L1. If

E = 2 x 105N/mm

2. Find the vertical displacement of L2 ,

15. The steel truss shown in fig. is anchored at A and supported on rollers at B. If the

truss is so designed that, under the given loading, all tension members are stressed to

100 N/mm2 and all compression members to 80 N/mm

2, find the vertical deflection of

point C. Take E= 2 x 105N/mm

2. Find also the lateral displacement of the end B.

1

2 m

A

B

E

20 kN

D

C

2 kN 2 kN 2 kN

300 300

P

Q R S

T

2 kN 2m 2m 2m

4 m 60 kN 4 m L1

U1 U2 U3

L3

60 0 60

0 60

0 60

0 60 0 60

0

L2

L0

4 m

8

2 1

4 5 6

3

9

7

4m 4m 4m

45 kN 45 kN

B

3 m

A

D C


Tutorial – 3 DIRECT & BENDING STRESSES

1. Explain limit of eccentricity and core of a section.

2. Distinguish between direct stresses and bending stresses.

3. Defined the kernel of a section. Obtain core of a Rectangular, Hollow rectangular,

circular, hollow circular section.

4. Limit of eccentricity defined in different sections Rectangular, Hollow rectangular,

circular, hollow circular.

5. A hallow rectangular masonry pier is 1.2 m X 0.8 m wide and 150 mm thick a

vertical load of 2 MN is transmitted in vertical plane bisecting 1.2 m side and at

an eccentricity of 100 mm from geometric axis of section. Calculate maximum.

and minimum stress intensities in section.

6. A column 800mm X 600 mm is subjected to eccentric load of 60 kN as shown in

fig.

7. What are maximum and minimum intensity of stress in section?

8. A shaft column of I- section 200 mm X 150 mm has a cross sectional area 4030

mm2 and minimum radius of gyration of 82.5 mm. A vertical load W N. acts

through the centroid of the section together with a parallel load of W/6 N. acting

through a point on the central line of the web distant 60 mm from the centroid.

Calculate the greatest allowable value of W if the maximum stress is not to

exceed 80 N/mm2. What is a minimum stress?

100mm

Y

Y

X X

800mm

100mm

600mm

LOAD POINT

60 mm

150mm

W/6 W

200 mm


9. A 20 m height masonary chimney is 2 m square at base and trapper to 1 m square

at top the tapped central flue is circular in cross- section and 1 m diameter at the

base. If the total weight of the brick work, about the base is 1300 kN find for what

uniform intensity of wind pressure an one face of chimney the stress distribution

the base just ceases to be wholly compressive.

10. A masonry dam of rectangular cross section 10 m high and 5 m wide has water up

to the top and its one side. If weight density of masonry is 21.582 kN /m2. Find

max. & min. stresses intensities at the base of dams.

11. A masonry trapezoidal Dam 4m. High, 1 m wide at its top and 3m. Wide at

bottom retains water and its vertical force. Determine the max. And min.

stresses.(a) When the reservoir is full (b) When the reservoir is empty. Take

weight density of masonary as 19.62 kN/m3.and of water as 10 kN/m

3.

12. A masonry dam of trapezoidal section is 10 m high. It has a top width of 1.5 m

and a bottom width of 6.5 m. The water face of the dam has a better of 1 in 10. If

the water level is at the top of the dam, find the maximum and the minimum

normal stresses at the base. Masonry weighs 22500 N/m3. And water weighs 9810

N/m3.

13. A mass concrete dam has a trapezoidal cross-section. The height above the

foundation is 64 m and its water face is vertical. The width at the top is 4.5 m.

calculate the necessary minimum width of the dam at its bottom, to ensure that no

tension should be developed when water is stored up to 60 m. Draw the pressure

diagram at the base of the dam, for this condition and indicate the max. Pressure

developed. Take density of concrete as 22.6 kN/m3 and density water as 9.81

kN/m3.

14. A trapezoidal masonry dam having 4 m top width, 8 m bottom width and 12 m

high, is retaining water upto a weight of 10 m. The density of masonry is 2000

kg/m3 and co-efficient of friction between the dam & soil is 0.55. The allowable

comp. stress is 343350 N/m2. Check the stability of dam.

15. A masonry retaining wall of trapezoidal section is 10m. Height and retains earth

which is level up to the top. The width at the top is 2 m. and at bottom at 8 m.

exposed face is vertical. Find maximum & minimum intensity of normal stress at

base.

16. A masonry wall 6 m high is of rectangular section 3 m wide and 1 m thick. A

horizontal wind pressure of 1.2 kN/m2

acts on 3m side. Find the maximum and

minimum stresses. Take unit weight of masonry 24 kN/m3 .


Tutorial – 4 COLUMNS AND STURD

1. A steel bar of solid cross-section is 60 mm in diameter. The bar is pinned at both ends

and subjected to axial compression. If limit of proportionality of material is 210 MPa

and E = 200 GPa, determine minimum length for which Euler's formula is valid. Also

determine Euler's buckling load if column has this minimum length.

2. Derive an expression for Euler‟s crippling load for column when one end is fixed and

other end is free. Compare ratio of the strength of a solid steel column to that of a

hollow of the same cross section areas. The internal diameter of the hollow column is

¾ of external diameter. The columns having the same length are hinged at the ends.

3. A hollow cast iron column 5 m long fixed at both ends and has external diameter of

300 mm. column support axial load of 1200 kN. Find internal diameter of the column.

Take F.O.S. = 5, fc= 500 N/mm2 and α = 1/1600.

4. Find greatest length of mild steel rod 30 mm x 30 mm which can be used as a

compressive member with one end fixed and other end hinged to carry a working load

of 70 kN. Allow a factor of safety 3. Taken α = 1/7500, fc= 300 N/mm2.

5. A hollow CI column 300 mm external diameter and 40 mm thick, is 8 m long and

hinged at both ends. Find Euler and Ranking‟s critical loads. For what length of

column, both critical load are equal fc= 600 N/mm2, and α = 1/1600, E = 100k N/mm

2.

6. A hollow cast iron column 200 mm. outside diameter and 25 mm thick is 6.5 long has

both the ends fixed. Determine safe Rankine‟s load. Factor of safety = 5; α = 1/1600,

fc= 550 N/mm2.

7. Compare the ratio of the crippling load of solid steel column to that of a hollow steel

column of same cross section area. The internal diameter of the hollow column is ¾ of

external diameter both columns have same length and are fixed at both ends. Use the

Euler‟s formula.

8. One I section joist shown in fig, 8 m long is used as a strut with both end fixed. What

is Euler‟s crippling load. E= 200 kN/mm2.

9. A hollow cast iron column 6 m. long is fixed at both ends, and has an external

diameter of 400 mm. find the internal diameter of column if it supports an axial load of

1000 kN. Factor of safety = 5; α = 1/1600, fc= 550 N/mm2.

250

25 500

25

All Dimension in mm


Tutorial 5 Arches, Cables and suspension bridge.

1. A three hinged parabolic arch span 40 m and rise 10 m carries a load of 15 kN at

quarter span. Calculate total at the hinged.

2. A three hinged arch has a span of 30 m and a rise of 8 m. the arch carries UDL of

15kN/m on the left half of the span. Determine maximum B.M.

3. A three hinged parabolic arch of span 40 m rise 12 m. it is subjected to a point load

15 kN acting at a distance of 10 m from the left support. Draw SFD and BMD. Also

determine radial shear and normal thrust under point load.

4. A parabolic arch hinged at springing and crown has a span of 18 m. The central rise

of arch is 4.2 m it is loaded with UDL of 11 kN/m on the 9 m length.

a. The direction and magnitude of reaction at the hinges.

b. The bending moment, normal thrust, and shear at 4 m and 15 m from left.

5. A symmetrical 3- hinged parabolic arch has a span 20 m. it carries UDL of

intensity10 kN/m over the entire span and a point load 40 kN at 5 m from left

support. Compute the reactions. Also find BM, radial shear and normal thrust at a

section 5 m from left end take central rise a 4 m.

6. A three hinged parabolic arch of 20 mm span and 4 m central rise carries a point load

of 150 kN at 4 m from left side support. Calculate Normal thrust and shear force at

section under load. Draw BMD.

7. Prove that bending moment at any section will be equal to zero for a parabolic three

three hinged arch subjected to UDL over its entire span.

8. For semi-circular arch shown in fig. Determine (i) support Reaction (ii) bending

moment (iii) shear and axial thrust at point load location.

9. For given cable find elevations YB and Yd. Also Find The maximum Table in the

cable.

A B

4.8 m

C 50 kN

15 m 15 m

7.5 m

A

B

20 m

C

D

E 15 m

12 kN

4 kN

15 m 10 m 20 m

5 m

6 kN


Tutorial 6 THIN CYLINDER

1) A thin cylindrical shell of internal diameter d, wall thickness t and length l, is

subjected to internal pressure p. Derive the expression for circumferential stress

produced if the efficiency of the longitudinal joint is η.

2) A thin cylindrical shell of internal diameter d and wall thickness t, length l, is

subjected to internal pressure p. Derive the expression for change in volume of the

cylinder.

3) A thin cylindrical shell of internal diameter d, length l and thickness t is subjected

to internal pressure p. Prove that volumetric strain is equal to twice the

circumferential strain plus longitudinal strain.

4) A thin cylindrical shell has 100 mm internal diameter and wall thickness is 12

mm. It carries a steam pressure of 5 N/mm2, Find hoop stress and longitudinal

stress in the shell.

5) A boiler shell of 2 m diameter is made up of 20 mm thick M.S. Plate. The

efficiency of longitudinal circumferential joints is 70 % and 60 % respectively.

Calculate the safe pressure in the boiler if permissible tensile stress in the shell

material through the rivets is 100 N/mm2. Also determine the circumferential

stress in the solid plate section and longitudinal stress in the solid plate section

and longitudinal stress through the rivets.

6) A seamless thin cylindrical shell made of copper plates 5 mm thick is filled with

water under a pressure of 4 N/mm2. The internal diameter of the cylinder is 200

mm and length 800 mm. Find the change in the diameter and the length. Find also

the amount of water pumped inside the cylinder to maintain the same pressure if

the water is assumed to be incompressible.

7) A spherical vessel 3 m diameter is subjected to an internal pressure of 2 N/mm2.

Find thickness of the plate required. If maximum stress is not to exceed 8 N/mm2.

Take efficiency of the joint as 75%.

8) A thin cylinder is filled with fluid, which exerts pressure 2.0 N/mm2 on the wall.

If the diameter of cylinder is 1.2 m, length of 4.0 m and shell thickness of 20 mm.

Calculate the change in the volume of the cylinder. Assume E=2x105 N/mm

2 and

Poisson‟s ratio as 0.28.

9) A cylindrical vessel 2.5 m long and 400 mm in diameter with 8 mm thick plates is

subjected to an internal pressure of 2.5 MPa. Calculate the change in length,

change in diameter and change in volume of the vessel. Take E = 200 GPa and

Poisson‟s ratio = 0.3 for the vessel material.

10) A cylindrical shell has 4.0 meter length, 1.2 meter diameter and 12 mm thickness.

The shell is subjected to internal pressure of 3 N/ mm2.calculate maximum shear

stress and change in dimension of shell.


Tutorial-7 Fixed Beam

1) Give the advantages of fixed beam.

2) Find out fixed end moment for a fixed beam carrying uniformly distributed load for the

whole span.

3) Derive the equation for fixed end moment developed if one of the supports of a fixed

beam settles by amount „δ”.

4) Calculate a fixed end moment if left support of fixed beam is rotates clockwise by an

amount θ.

5) A fixed beam AB of span of 6 m carries a UDL of 30 kN/m over the entire span.

Find the fixed end moments by using first principal and draw SF and BM diagram.

Also locate the point of contra flexure.

6) Analyse a fixed beam as shown in fig.1. Draw bending moment diagram

7) A beam AB span of 7 m is fixed at A and B. it is loaded with UDL of 3 kN/m over

the entire span in addition to a concentration load of 5 Kn at 5 m from A. calculate

fixed end moment.

8) An encased beam of span 4 m carries a UDLof 8 kN/m and two points loads of 50

kN and 60 kN at 1 m and 2 m from left hand support. Find the fixed end moments

support reaction and draw SFD and BMD.

9) A fixed beam AB of span 10 m carries UDL of 80 kN/ m over 1/3 span from A. find

fixed end moment.

10) Analysis fixed beam as shown in fig. 2.

11) A beam AB of span 5 meter fixed at both ends carries a uniformly distributed load of

20kN/m over the whole span. The left end „A‟ rotates clockwise by 0.80

and right end

„B‟ sinks by 10 mm. Determine the fixed end moments and the reactions at the supports.

Draw also shear force and bending moment diagrams. Take E = 200 kN /mm2 and I = 10

x107

mm4.

4m 3m 1m

40 kN/m

A

C D

B

60 kN .m

3m 2m 2m

40 kN/m

A C D B

60 kN

1m

E


Tutorial-8 STRAIN ENERGY

1. Explain following Terms,

a) Resilience

b) Proof Resilience

c) Modulus of Resilience

2. Derive the formula for,

a) Strain due to gradual loading

b) Strain due to sudden loading

c) Strain due to impact loading

3. A 1500 mm long wire of 25 mm2 cross sectional area is hanged vertically. It receives a

sliding collar of 100 N weight and stopper at bottom end. The collar is allowed to full on

stopper through 200 mm height. Determine the instantaneous stress included in the wire

and corresponding elongation. Also determine the strain energy stored in the wire. Take

modulus of elasticity of wire as 200GPa.

4. A weight of 2 kN is dropped on to a collar at the lower end of vertical bar 3 m long and

28 mm in diameter. Calculate the maximum height of drop if the maximum instantaneous

stress is not exceeding 120 N/mm2. What is corresponding instantaneous elongation?

Take E = 2 x 105 N/mm

2

5. Determine the strain energy of a cantilever beam of span 2 m having size 20 mm width

and 60 mm depth. Take E = 200GPa.

a) When 1 kN concentrated load is placed at free end.

b) When total 1 kN load is uniformly distributed over the entire span.

6. Determine the strain energy stored due to in the beam for the simply supported beam

having span 3 m, loaded 10 kN and 2 m from the left support. Take E = 210 GPa and I =

72 x 104 mm

4

7. A solid shaft 120 mm diameters and 1.5 m long is used to transmit power from one pulley

to another. Determine the maximum strain energy that can be stored in the shaft. If the

maximum allowable shear stress is 50 MPa. Take shear modulus as 80 GPa.

8. A thin strip of steel 5 mm wide and 0.5 mm thick is wound round a cylinder 500 mm in

diameter. Find the strain energy stored in the strip. E = 2 x 105 N/mm

2

9. A simply supported beam AB of span 5 m carries a U.D.L. of 5 kN/m over its entire span.

Determine the strain energy stored due to bending in the beam. Take E = 200 GPa, I =

200 cm4.

10. An unknown weight fall through a height of 10 mm on a collar rigidly attached to the

lower end of a vertical bar 5 m long and 600 mm2

cross section. If the maximum

extension of the rod is to be 2 mm. what is the corresponding stress and magnitude of the

unknown weight.

11. A steel bar 1.2 m long and rectangular in section 40 mm x 80 mm is subjected to an axial

load of 2 kN. Find the maximum stress if, (i) the load is applied gradually (ii) the load is


applied suddenly, and (iii) The load is applied after falling through a height of 10 cm.

What are the strain energies in each of the above cases; Take E = 200 GPa.

12. An axial pull of 100 kN is applied to a steel bar 2 m long and 1000 mm2 in cross section.

If modulus of elasticity of material is 200 KN /mm2. Find the maximum instantaneous

stress, maximum instantaneous extension, strain energy and modulus of resilience.


Schedule of submission of A1, A2, A3, and A4

Structural Analysis -1

B.E-IIrd

(4th

SEMESTER)

Subject Code : 2140603 YEAR- January 2019

Name of student:

Enrollment No:

Sr. No Description Date Of

submission

1) Tutorial – 1 (Example – 1 to 10) 02/01/2019

2) Tutorial – 1 (Example 10-12 (1 to 12 ) 09/01/2019

3) Tutorial – 1 Example 12 (12 to 20) + Tutorial-8 strain energy

(Example – 1 – 04) 16/01/2019

4) Tutorial-8 strain energy (Example – 05 to 12) 23/01/2019

5) Tutorial – 6 Thin cylinder 30/01/2019

6) Tutorial – 2 (Example 01 to 8) 05/02/2019





11) Tutorial – 4 (Example 05 to 9) + Tutorial 7 Example 1- 3 12/03/2019




15) Final Submission 09/04/2019


Schedule of submission of A1, A2, A3, and A4

Structural Analysis - 1

B.E-IIrd

(4th

SEMESTER)

Subject Code : 2140603 YEAR- January 2019

Name of student:

Enrollment No:

Sr. No Description Date Of

submission

1) Tutorial – 1 (Example – 1 to 10) 28/12/2018

2) Tutorial – 1 (Example 10-12 (1 to 12 ) 02/01/2019

3) Tutorial – 1 Example 12 (12 to 20) + Tutorial-8 strain energy

(Example – 1 – 04) 09/01/2019

4) Tutorial-8 strain energy (Example – 05 to 12) 16/01/2019

5) Tutorial – 6 Thin cylinder 23/01/2019






11) Tutorial – 4 (Example 05 to 9) + Tutorial 7 Example 1- 3 05/03/2019




15) 02/04/2019

16) Final Submission 09/04/2019

Date post:	25-Mar-2020
Category:	Documents
Upload:	others
View:	35 times
Download:	0 times

GOVERNMENT ENGINEERING COLLEGE DAHOD APPLIED …GOVERNMENT ENGINEERING COLLEGE DAHOD Applied...

Documents