CE2352 Design of Steel Structures Two Marks with Answers for May June 2013 Exam

CE2352 Design of Steel Structures

2013 Edition

TWO MARKS - QUESTIONS & ANSWERS


UNIT – i - Connections – riveted, welded & bolted


1. Mention the advantages and disadvantages of steel structures?

Advantages:

ü Ability to resist high loads

ü Due to its high density, steel is completely non-porous

ü Durability

ü Easy to disassembling or replacing some steel members of a structure

Disadvantages:

ü Corrosion

ü At high temperature steel loses most of its strength, leading to deformation or failure

2. What is meant by Girder?

Girder means a major beam frequently at wide spacing that supports small beams.

3. What is meant by joists?

It is a closely spaced beam supporting the floors and roofs of buildings

4. What is meant by Purlins?

It is a roof beam usually supported by trusses

5. What is meant by Rafters?

It is a roof beam usually supported by purlins

6. What is meant by Lintel?

It is a beam over window or door openings that support the wall above.

7. What is Girts?

It is horizontal wall beams used to support wall covering on the side of an industrial building

8. What is meant by Spandrel beam?

It is beam around the outside perimeter of a floor that support the exterior walls and the outside edge of the floor

9. Name the different types of connections?

ü Riveted connections

ü Welded connections

ü Bolted connections

ü Pinned connections

10. Name the types of riveted connections?

ü Lap Joint - single riveted and double riveted

ü Butt joint – single cover and double cover

11. What is meant by rivet value?

The least of the strengths in shearing and bearing is the rivet value

12. What is meant by gauge distance?

The perpendicular distance between two gauge lines, is called gauge distance

13. Name the different modes of failure of a riveted joint?

ü Tearing failure of the plate

ü Shear failure of the plate

ü Shear failure of the rivet

ü Bearing failure of the rivet

ü Splitting failure of plate

14. As per the American practice where the neutral axis lie in the rivet group?

It is assumed that the line of rotation lies at a distance of 1/7 th of the effective bracket depth from the bottom of the bracket

15. What are the factors that govern will govern the structural design?

ü Foundation movements

ü Elastic axial shortening

ü Soil and fluid pressures

ü Vibration

ü Fatigue

ü Impact (dynamic effects)

ü Erection loads

16. What are the load combinations for the design purposes?

ü Dead load + Imposed Load (Live load)

ü Dead Load + Imposed Load + Wind Load or earthquake load

ü Dead Load + Wind Load or Earthquake load

17. What are the steps involved in structural design?

ü Forces or loads

ü Structural arrangement and material selection

ü Analyzing internal stresses

ü Proportioning of members

18. Which type of steel is most commonly used in general construction? Why?

Mild Steel is most commonly used in general construction because of its durability

and malleability

19. What are Black bots? Where are they used?

Black bolts made from M.S shank left unfinished – remain loose in holes resulting in large deflections. It is used during erection and for temporary structures

20. How the rolled steel beams are classified?

ü Indian Standard junior beams (ISLB)

ü Indian Standard light beams (ISLB)

ü Indian Standard medium weight beams (ISMB)

ü Indian Standard wide flange beams (ISWB)

21. Define permissible stresses and Working stresses.

Permissible stresses = clip_image002

Working stresses: The stresses used in practical design are working stresses and they should never exceed the permissible stresses specified by codes.

22. Explain ISLB 200?

ISLB 200 means Indian Standard light gauge beams of depth 200mm

23. Name the types of beam connections?

ü Framed connections

ü Seated connections – Stiffened connections and Unstiffened connections

24. What is meant by framed connections?

A framed connection is the one when a beam is connected to girder or a stanchion by means of two angles placed on the two sides of the web of the beam

25. When the seated beam connections are preferred and name the types?

When a beam is connected to the flange (or the web) of a steel stanchion, the width of the flange (or the depth of the web) may be insufficient to accommodate the connecting angles, in such cases framed connection is not suitable and seated connection is preferred.

26. What is unstiffened seat connection?

The seated connection is a horizontal angle with its horizontal leg at its top is used to receive the beam on it, in such a case it is called unstiffened seat connection

27. What is stiffened seat connection?

In addition to the seat angle, a web cleat is provided when the beam is connected to a beam and a flange cleat is used when the beam is connected to a stanchion. The angle cleats are essential because they keep the beam stable in a vertical position and prevent it from lateral buckling

28. What is meant by throat thickness?

It is the perpendicular distance from the root to the hypotenuse of the largest

isosceles right-angled triangle that can be inscribed within the weld cross-section.

Throat thickness = 0.7 x size of the weld

29. What is plug weld and slot weld?

Slot weld is one of the type of weld used to join the two touching contiguous

components by a fillet weld round the periphery of a slot in one component so as to join it the surface of other component.

Plug weld is made by filling in a hole in one part with filler metal so as to join it to the

contiguous part exposed through a hole.

30. Mention the advantages and disadvantages of welded connections?

Advantages:

ü Economy

ü Rigidity

ü Aesthetic effect

ü Versatility

Disadvantages:

ü Requires skilled labour

ü Joints are over rigid

ü Difficult to inspect

31. State the common defects in welding

ü Incomplete fusion

ü Incomplete penetration

ü Porosity

ü Slag inclusions

ü Cracks

ü Under cutting

32. Name the types of bolted connections?

ü Ordinary unfinished 0r black bolts

ü Turned and fitted bolts

ü High strength bolts

33. Write the advantages of high strength bolts?

ü As there is no slip between the plates, the joint is rigid

ü Alternating loads cause little variation of the stresses in the bolts; hence fatigue strength is also high.

ü No shearing or bearing stresses occur in bolts.

ü High strength of the joint due to high frictional resistance is obtained.

34. Write down the interaction equation?

clip_image004

35. How will you calculate the number of rivets?

clip_image006

where P is the pull or push carried by the member.


UNIT – II - TENSION MEMBERS

1. Tie member – Explain.

Tie member or a tension member is a structural element carrying an axial tensile force. For the tensile force to be axial it is necessary that the load be applied through centroid of the section of the member. But under axial tension the member gets straightened and eccentricity of the force decreases. The member is almost straight at the yield point and the distribution of the stress over the section becomes uniform.

2. How the tension members are classified?

It is classified according to its shape and size and it depends upon the type of structures.

ü Wires and cables – Used in hoists, derricks, suspenders in suspension

bridges

ü Rods and bars – Used in radio tower, small spanned roof trusses with

different cross-sections such as round, rectangular or square

3. What is meant by single section member?

Structural sections such as I-section, T-section, angle, and channel are used as tension members. As the structural shapes provide more rigidity than cables or rods, their buckling tendency under compression load is reduced and so can be used where reversal of stress takes place.

4. Under what circumstances you would go for Built-up members?

When single structural sections fail to provide required strength and stiffness to carry tension as well as compression in case of reversal of stresses, built-up members are used.

5. How the tension members are selected?

It depends upon the various factors such as type of fabrication, type of structure, type of loading, i.e. whether the member undergoes reversal of stresses, and the maximum tension to be carried by the member.

 
  clip_image008

6. Sketch the different forms a single section member
 
  clip_image009

7. Sketch the different forms Built-up members.

Built up members

8. How is net effective area of single angle used as tension member calculated?

Net effective area = A1 + A2K

A1- Net area of connected leg

A2- area of outstanding leg

K = clip_image011

9. What is net sectional area of a tension member? How it is calculated in chain riveting?

The gross sectional area of the tension member minus the sectional area of the maximum number of rivet/bolt holes is known as net sectional area.

In case of chain riveting,

anet= (b – nd) t

10. What is Lug angle?

A larger length of the tension member and the gusset plate may be required sometimes to accommodate the required number of connection rivets. But this may not be feasible and economical. To overcome this difficulty lug angles are used in conjunction with main tension members at the ends. It provides extra gauge lines for accommodating the rivets and thus enables to reduce the length of the connection. They are generally used when the members are of single angle, double angle or channel sections.

11. What are the main objectives of the lug angles?

ü They produce eccentric connections, due to rivets placed along lug angle. The centroid of the rivet system of the connection shifts, causing eccentric connection and bending moments.

ü Stress distribution in the rivets connecting lug angles is not uniform. It is preferred to put a lug angle at the beginning of the connection where they are more effective and not at the middle or at the end of the connection.

ü Rivets on the lug angles are not as efficient as those on the main member. The

out-standing leg of the lug angle usually gets deformed and so the load shared by the

rivets on the lug angles is proportionately less.

12. What is meant by Tension splice?

Splicing of tension members is necessary when the required length of the member is more than the length available or when the member has different cross-sections for different parts of its length. If actual member is to be of greater length, two or more lengths shall have to be spliced at the joints.

  1. What is the net effective area of a pair of angles placed back to back connected by one leg of each angle subjected to tension?

Anet = A1 + A2 K

A1 - effective cross – section area of connected legs

A2 – Gross area of outstanding legs

K = clip_image013

  1. What is the permissible stress in axial tension?

As per IS: 800 – 1984, the permissible stress in axial tension

sat = 0.6 fy N/mm2

fy = minimum yield stress in steel in N /mm2.

  1. How will you join the member of different thickness in a tension member?

When tension member of different thickness are to be jointed, filler plates may be used to bring the member in level.

  1. What happens when a single angle with one leg is connected to a gusset plate, which is subjected to an eccentric load?

The rivets connecting the angle to the gusset plate does not lie on the line of action of load. This gives rise to an eccentric connection due to which the stress distribution becomes non-uniform. The net cross-sectional area of such a section is reduced to account for this non-uniform stress distribution resulting from eccentricity.

  1. What is the allowable stress in axial tension for channel section?

The allowable stress in axial tension for channel section is depends upon the diameter of the section

Diameter

sat = 0.6 fy N/mm2

Upto 20mm

150

20mm to 40 mm

144

Over 40 mm

138

  1. What are tacking rivets? Why are they essential in compression members?

Rivets used to connect long length of members to reduce the effective length of individual part

  1. Write down the Steinman’s formula

Anert = clip_image015

Where n = no. of rivets in the section considered

m= no. of zig zags or inclined lines.

  1. What will be the maximum pitch when the angles are placed back to back?

The maximum pitch when the angles are placed back to back is 1mm.


UNIT – III - compression members


  1. What do you mean by compression members?

Compression members are the most common structural elements and it is termed as columns, struts, posts or stanchions. They are designed to resist axial compression.


2. Name the modes of failures in a column.

ü Failure of the cross-section due to crushing or yielding

ü Failure by buckling, due to elastic instability

ü Mixed mode of failure due to crushing and buckling


3. Define slenderness ratio

It is defined as the ratio of effective length l of the column to the least radius of gyration r of the column section.


4. Classify the columns according to the slenderness ratios.

ü Short columns - l/r <60

ü Medium columns - 60< l/r <100

ü Long columns - l/r >100


5. Distinguish column and strut

Columns are the vertical members which carry the loads to the beams, slabs etc, generally they are used in ordinary buildings.

Struts are commonly used for compression members in a roof truss; it may either be in vertical position or in an inclined position.


6. What is meant by stanchions?

These are the steel columns made of steel sections, commonly used in buildings.


7. What is Post?

It is loosely used for a column, but in truss bridge girders, end compression members are called end posts.


8. What is a boom?

It is the principal compression member in a crane.

9. State the assumptions that made in Euler’s theory.

ü The axis of the column is perfectly straight when unloaded.

ü The line of thrust coincides exactly with the unstrained axis of the strut.

ü The flexural rigidity EI is uniform

ü The material is isotropic


10. Why the lateral systems are provided in compound columns?

If the plates are not connected throughout their length of the Built up sections, lateral systems may be provided, which act as a composite section. In such cases the load carrying elements of the built-up compression member in the relative position, without sharing any axial load. However when the column deflects, the lateral system carries the transverse shear force.


11. Name the lateral systems that are used in compound columns and which is the mostly used one?

Lacing or latticing, Battening or batten plates, perforated cover plates.

Lacing or latticing is the most common used lateral system and the sections are flats, angles and channels.


12. What will be the thickness for the single and double lacing bars?

The thickness of flat lacing bars shall not be less than one-fortieth of the length between the inner end rivets or welds for single lacing, and one-sixtieth of the length for double lacing.


13. What is the purpose of providing battens in compound steel columns?

Batten plates consist of flats or plates, connecting the components of the built-up columns in two parallel planes. These are used only for axial loading. Battening of the composite column should not be done if it is subjected to eccentric loading or a applied moment in the plane of battens.


14. What is the thickness of a batten plate?

The thickness of batten plate shall not be less than one fiftieth of the distance between the inner most connecting lines of rivets or welds. This requirement eliminates lateral buckling of the batten.


15. Where the perforated cover plates are used and mention its advantages?

They are mostly used in the box sections, which consist of four angle sections so that

the interior of column remains accessible for painting and inspection.

Advantages:

ü They add to the sectional area of column and the portions beyond the perforation share axial load to the extent of their effective area.

ü There is economy and fabrication and maintenance

ü Perforations conveniently allow the riveting and painting work on the inside portion.

16. Name the types of column base?

ü Slab Base, which is a pinned base.

ü Gusseted base, which is a rigid base.


17. State the purpose of column base?

The base of the column is designed in such a way to distribute the concentrated column load over a definite area and to ensure connection of the lower column end to the foundation. It should be in adequate strength, stiffness and area to spread the load upon the concrete or other foundations without exceeding the allowable stress.


18. Give the difference between slab base and gusseted base for steel columns.

Slab base is a thick steel base plate placed over the concrete base and connected to it through anchor bolts. The steel base plate may either be shop-welded to the stanchion, or else can be connected at the site to the column through cleat angles. The column is faced for bearing over the whole area.

In a gusseted base, part of the load is transmitted from the stanchion through the gusseted base plate. The gussets and stiffeners support the base slab against bending and hence a thinner base plate can be used. The gussets serve for more or less uniform transmission of the force field from the column to the base plate. The gussets itself resists the bending as double cantilever beam supported on flanges of the column.


19. What is slab base and for what purpose is it provided?

The base plate connected to the bottom of the column to transfer over wider area is known as slab base. Column end is machined to transfer the load by direct bearing. No gusset materials are required.


20. When the slenderness ratio of compression member increases, the permissible stress decreases. Why?

The section must be so proportioned that it has largest possible moment of inertia for the same cross-sectional area. Also the section has approximately the same radius of gyration about both the principal axes.


BEAMS


  1. What is a beam?

A beam is a structural member, which carries a load normal to the axis. The load produces bending moment and shear force in the beam.


  1. What is meant by castellated beam?

A rolled beam with increased depth is to be castellated. To obtain such sections, a zigzag line is cut along the beam by an automatic flame-cutting machine. The two halves thus produced are rearranged so that the teeth match up and the teeth are then welded together.


  1. How the beams are failed?

ü Bending failure

ü Shear failure

ü Deflection failure

The designs are based on these three failures which are to be determined.


  1. What do you mean by bending failure?

Bending failure may be due to crushing of compression flange or fracture of the tension flange of the beam. Instead of failure due to crushing, the compression flange may fail by a column like action with side ways or lateral buckling. Collapse would follow the lateral buckling.


  1. What is the maximum deflection that to be allowed in steel beams?

The deflection of a member, shall not be such as to impair the strength or efficiency of the structure and lead to finishing. The deflection is generally should not exceed 1/325 of the span.


  1. What is web crippling?

Web crippling is the localized failure of a beam web due to introduction of an excessive load over a small length of the beam. It occurs at point of application of concentrated load and at point of support of a beam. A load over a short length of beam can cause failure due to crushing and due to compressive stress in the web of the beam below the load or above the reaction. This phenomenon is also known as web crippling or web crushing.


  1. What are laterally supported beams?

The beams which are provided with the lateral supports either by embedding the compression flange in the concrete slab or by providing effective intermediate (support) restraints at a number of points to restrain the lateral buckling is called laterally supported beams.


  1. Mention the advantages of using rolled steel wide flange section as beams

ü More section modulus

ü Lesser area

ü Economical


  1. Why does buckling of web occur in beams?

ü Diagonal compression due to shear

ü Longitudinal compression due to bending

ü Vertical compression due to concentrated loads



  1. What are the permissible stresses used in the beams?

The permissible stresses, which are used in the beams are bending and shear stress.

Bending Stress

ü For laterally supported beams,

clip_image017

ü For laterally unsupported beams,

clip_image019 , Where n is assumed to be 1.4

Shear Stress

clip_image021, clip_image023 = maximum permissible shear stress


  1. Under what situations the plated beams are used?

ü When a bending moment is large which cannot be resisted by the largest available rolled beam section

ü The depth of the beam is restricted due to headroom requirements.


  1. Why intermediate stiffeners are required for plate girders?

The web of the plate girder relatively being tall and thin it is subjected to buckling. Hence it is stiffened both vertically and horizontally using intermediate stiffeners.


  1. What do you mean by curtailment of flanges?

The section of a plate girder is to be designed first at mid span. The bending moment will goes on decreasing towards the supports. Hence the flange plates, provided at the maximum section can be curtailed.


  1. What is the purpose of providing the bearing stiffener?

ü It prevents the web from crushing and buckling sideways, under the action of concentrated loads

ü It relieves the rivets connecting the flange angles and web, from vertical shear.


  1. Name the components of a plate girder.

ü Web plate

ü Flange plate

ü Flange angles

ü Web splice plates

ü Flange splice plates

ü Vertical or transverse stiffeners

ü Bearing stiffeners

ü Longitudinal or horizontal stiffeners

ü End bearings or end connections


  1. Mention the basic design assumptions of a plate girder?

ü The web plate resists the shear force.

ü The shear stress is uniformly distributed over whole cross sectional area of web.

ü The flanges resist the bending moment


  1. Where the plate girders are used?

The plate girders are used in the buildings where the span is more and heavy loads are expected and in the bridges. Most commonly they are used in the bridges.


  1. What are the methods that are adopted to determine the flange design?

ü Flange area method

ü Moment of inertia method

The former method is an approximate method, which is used for determining the trial section. In this method, it is assumed that the stress distribution in the tension and compression

flanges is uniform, whereas in the latter case it is the exact method and is recommended by the IS code. Generally, the section designed by the flange area method is checked by this method.


  1. What is the economical depth of a plate girder?

The economical depth of a plate girder is

clip_image025, where clip_image027= permissible bending stress in compression in N/mm2.

clip_image029 = thickness of the web plate.


  1. The pitch of the rivets connecting cover plates with flanges of rolled steel beam is designed for what force?

These rivets are designed for horizontal shear between the flange plate and flange angles. Since the vertical load is transferred by the flange plates to the flange angles by direct bearing, there will be no vertical shear due to the vertical load. Here the rivets will be in single shear.


UNIT – V – ROOF TRUSSES AND INDUSTRIAL BUILDINGS
  1. Name the types of roofing systems.

ü Flat roofing consists of either RCC construction or RSJ slab construction

ü Sloping roofing


  1. Where the steel roof trusses are used?

Industrial buildings, workshop buildings, storage godowns, warehouse and even for residential buildings, school buildings, offices where the construction work is to be completed in a short duration of time.


  1. Mention the advantages of a roof truss.

ü Its mid-span depth is the greatest specially where bending moment in the span is the maximum

ü Great economy.

ü Sloping faces of trusses facilitate in easy drainage of rainwater.


  1. What is the factor that is considered in the roof truss and why?

The factor, which is considered in the roof truss, is pitch, it is defined as the ratio of the span length to the depth of the truss, is governed by the roofing material and other requirements such as ventilation and light.


  1. How the trusses are classified according to the pitch?

ü Small pitch - span depth ratio is more than 12 m

ü Medium pitch - span depth ratio is between 5m to 12 m

ü Large pitch - span depth ratio is 5 or less.


  1. Sketch the various types of roof truss.

clip_image031


  1. Name the components of a roof truss.

ü Principal rafter or top chord

ü Bottom chord or main tie

ü Ties

ü Struts

ü Sag tie

ü Purlins

ü Rafters

ü Ridge line

ü Eaves

ü Panel points

ü Roof coverings

ü Shoe angle

ü Base plate, anchor plate and anchor bolts


  1. What is gantry girder and what are the forces that are acting on it?

A gantry girder, having no lateral support in its length, has to withstand vertical loads from the weight of the crane, hook load and impact and horizontal loads from crane surge.


  1. What is meant by purlins?

Purlins are structural members which are supported on the principal rafter, and which run transverse to the trusses. The span of the purlins is equal to the center-to-center spacing of the trusses. The purlins support the roof covering either directly or through common rafters. They are usually made of either an angle section or a channel section and are therefore subjected to unsymmetrical bending.


  1. Why the bracings are provided?

Bracing is required to resist horizontal loading in pin-jointed buildings, including roof trusses. Bracing of roof trusses and supporting columns provide still rigid structure. When wind blows normal to the inclined surface of the trusses, it is efficiently resisted by all the members of the truss and the wind forces are transferred to the supports at the ends of the truss.


  1. Name the most common roof covering materials.

ü Slates

ü Tiles

ü Lead sheets

ü Zinc sheets

ü Glass

ü Corrugated aluminium sheets

ü Galvanized corrugated iron sheets (G.I. sheets)

ü Asbestos cement sheets (A.C. sheets)


  1. Write the equation to calculate the design wind pressure.

Design pressure is clip_image033

clip_image035 = Basic wind speed in m/s at 10 m height

clip_image037= Probability factor (or risk coefficient)

clip_image039= Terrain, height and structure size factor

clip_image041=Topography factor


  1. Mention some of the requirements of a good joint.

ü The line of thrust should pass through the C.G of the rivet group and the rivets should be symmetrically arranged about this line.

ü For a tension member, the rivets should be so arranged that the area of the member joined is not reduced more than necessary.

ü The number and the diameter of rivets should be sufficient to develop the maximum stresses induced in all the members at the connection.

ü Members should be straight and bolts used to draw them together before the rivets are driven.


14. What are the conditions that to be satisfied for the end supports?

ü The size of base plate should be sufficient so that the bearing pressure does not exceed the permissible value.

ü Anchor bolts should be provided at one end to accommodate the thermal expansion of the truss.

ü The lines of forces in rafter, bottom tie and vertical end reaction meet at a point.


  1. Where the gantry girders are used?

Gantry girders or crane girders carry hand operated or electric over head cranes in industrial buildings such as factories, workshops, steel works etc., to lift heavy materials, equipment etc., to carry them from one location to the other, within the building.


  1. Sketch the various forms of gantry girders.

clip_image043

Forms of gantry girders


  1. What is drag force?

This is caused due to the starting and stopping of the crane bridge moving over the crane rails as the crane m0oves longitudinally, i.e. in the direction of gantry girders.


  1. What is the permissible deflection where the electrically overhead cranes operated over 500kN?

The maximum vertical deflection for crane girder, under dead and imposed loads shall not exceed L/1000, where L is the span of the crane runway girder.


  1. Define shoe angle.

It is a supporting angle provided at the junction of the top and bottom chords of a truss. The reaction of the truss is transferred to the supports through the shoe angle. It is supported on the base plate.


  1. What is panel point?

These are the prominent points along the principal rafter, at which various members (i.e. ties and struts) meet. The distance of the principal rafter between any two panel point is termed as panel.


EC2252 Communication theory Important Question–May / June 2013

Anna University

EC2252 Communication theory

Important Questions


Unit 1.Amplitude modulation systems.

1)Explain AM envelope.

2)Write about AM power distribution.

3)Explain square law modulator.

4)Write about transistor modulator.

5)Explain FDM technique.


Unit 2.Angle modulation systems.

1)Explain phase modulation with neat diagram.

2)Draw and explain generation of wideband FM.

3)Explain Armstrong method of FM generation.

4)Write about Foster seely discrminator.

5)Write the detection of FM signal


Unit 3.Noise theory.

1)Write about Random process with types.

2)Explain the properties of P.D.F.

3)Explain the types of noise.

4)What is noise figure with its derivation.

5)Explain the gaussion process.


Unit 4.Performance of cw modulation systems

1)Write the characteristics of receiver.

2)Derive the average power of message signal.

3)Explain noise in FM system.

4)Write about FM thershold effect.

5)Draw the equivalent circuit of preemphasis.


Unit 5.Information theory.

1)Explain the concept of amount of information.

2)Problem based on Huffman coding.

3)Problem based on LZ coding.

4)Explain bandwidth ,SN trade off.

5)Explain rate distortion theory.

CE 2252 STRENGTH OF MATERIALS–Question Bank–2013 V+ Edition

Anna University

Department of Electrical and Electronics Engineering

CE 2252 / STRENGTH OF MATERIALS QUESTION BANK – 2013 Edition

DEPARTMENT: CIVIL

SEMESTER: IV

SUBJECT CODE / Name: CE 2252 / STRENGTH OF MATERIALS


Download: http://www.vidyarthiplus.com/vp/Thread-CE2252-Strength-of-Materials-University-Question-Bank-2013-Edition


UNIT – I - ENERGY PRINCIPLES

PART – A (2 Marks)

1. A beam of span 4 m is cantilever and subjected to a concentrated load 10 kN at free end. Find the total strain energy stored. Take the Flexural rigidity is EI.

(AUC Apr/May 2010)

2. Write down Maxwell’s reciprocal theorem. (AUC Apr/May 2010)

3. Write down the expression for strain energy stored in a bar of cross sectional area A

and length ‘l’ and subjected to a tensile load ‘W’. (AUC Nov/Dec 2010)

4. State Maxwell’s reciprocal theorem. (AUC Nov/Dec 2010, Apr/May 2011 & 2012)

5. State the principle of virtual work. (AUC Apr/May 2011)

6. Calculate the strain energy stored in the beam shown in fig. EI constant.

clip_image002 (AUC Nov/Dec 2011)

7. State Castigliano’s first theorem. (AUC Nov/Dec 2011)

8. Find the deflection at free end of the cantilever of 1m span carrying a point load of 10kN

at free end. EI=25000kNm2 using principle of virtual work. (AUC Apr/May 2012)

9. Define strain energy density.

10. Define proof resilience.

11. Define the terms: Proof resilience and Modulus of resilience.

12. Derive relation for strain energy due to shear.

13. Define the term Poisson’s ratio and Bulk modulus.

14. Explain the effect of change of temperature in a composite bar.

15. What is meant by Strain energy?

16. Write down the equilibrium equations?

17. Define modulus of resilience.

18. Define unit load method.

19. Write down the different typed of loads due to different stresses?

20. Compare the unit load method and Castigliano’s first theorem

PART – B (16 Marks)

1. For the beam shown in Fig, find the deflection at C and slope at D (AUC Apr/May 2010)

I = 40 x 107 mm4

E = 200 GPa.

clip_image004

2. For the truss shown in Fig, find the horizontal movement of the roller at D AB, BC, CD area = 8 cm2 (AUC Apr/May 2010) AD and AC = 16 cm2

E = 2 x105 N / mm2.

clip_image006

3. Derive the expression for strain energy in Torsion of a circular shaft of length ‘I’ and radius ‘R’ subjected to a Torque ‘T’ producing a twist ‘ θ ’ in the length of the shaft for the following cases. (AUC Nov/Dec 2010) (i) Solid circular shaft and

(ii) Hollow circular shaft, with an external radius ‘R’ and internal radius ‘r’.

4. i) An axial pull of 40 kN is suddenly applied to a steel rod 2m long and 1000mm2 in cross section. Calculate the strain energy that can be absorbed if E = 200 GN/m2.

ii) A cantilever of rectangular section breadth b, depth d and of length l carries uniformly distributed load spread from free end to the mid section of the cantilever. Using Castigliano’s theorem find: Slope and deflection due to bending at the free end. (AUC Nov/Dec 2010)

5. A beam 4m in length is simply supported at the ends and carries a uniformly distributed load of 6 kN/m length. Determine the strain energy stored in the beam. Take E = 200 GPa and I = 1440 cm4. (AUC Apr/May 2011)

6. 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 Castigliano’s theorem, determine the deflection at the centre of the beam. (AUC Apr/May 2011)

7. For the beam shown in fig. find the slope and deflection at ‘C’. (AUC Nov/Dec 2011)

clip_image008

8. i) For the truss shown in fig. find the total strain energy stored. (AUC Nov/Dec 2011)

clip_image010

E : 2 × 105 N/mm2

Area : AB : 100 mm2

BC : 100 mm2

AC : 80 mm2

ii) For the truss shown in fig. find the vertical deflection at ‘C’. (AUC Nov/Dec 2011)

clip_image012

Cross sectional area of

all the members : 100 mm2

E = 2 × 105 N/mm2

9. Determine vertical and horizontal deflection of joint C as shown in fig. Using principle of virtual work. Take E=200kN/mm2 and A=600mm2 for all the members.

(AUC Apr/May 2012)

clip_image014

10. Using Castigliano’s theorem, find the slope and deflection at B for the cantilever beam

shown in fig. Take E=2 x 105 N/mm2 and I = 1 x 108 mm4. (AUC Apr/May 2012)

clip_image016

11. i. Derive a relation for strain energy due to shear force. (4m)

ii. Derive a relation for maximum deflection of a simply supported beam with uniformly distributed load over entire span. Use strain energy method. (12m)

12. Determine the deflection at C of the beam given in Fig. Use principal of virtual work.

clip_image018

13. The external diameter of a hollow shaft is twice the internal diameter. It is subjected to pure torque and it attains a maximum shear stress ‘τ’. Show that the strain energy stored

clip_image0195t 2

per unit volume of the shaft is

16C

. Such a shaft is required to transmit 5400 kw at 110

r.p.m. with uniform torque, the maximum stress not exceeding 84 MN/m2. Determine i. The shaft diameters (8m)

ii. The strain energy stored per m3. Take C = 90 GN/m2. (8m)

13. Using Castigliano’s theorem, determine the deflection of the free end of the cantilever beam shown in fig. A is fixed and B is free end Take EI = 4.9 MN/m2

clip_image021

15. A beam 4m in length is simply supported at the ends and carries a UDL of 6 kN/m length over the entire length. Determine the strain energy stored in the beam. Take E = 200

GN/m2 and I = 1440 cm4.

16. A beam simply supported over a span of 3m carries a UDL of 20 kN/m over the entire span. Taking EI = 2.25 MNm2 and using Castigliano’s theorem, determine the deflection at the centre of the beam.

17. A continuous beam of two equal spans L is uniformly loaded over its entire length. Find

the magnitude R of the middle reaction by using Castigliano’s theorem.

18. Determine the vertical displacements of both lower points C and D for the pin jointed frame shown in fig. The cross sectional area of all members is 130mm2 and the modulus of elasticity is 200 kN/mm2. Determine the magnitude of an additional vertical load placed at D necessary to increase the deflection at C by 50%.

clip_image023

19. A simply supported beam of span “l” carries an uniformly distributed load of w per unit

length over the entire span. Using Castigliano’s theorem determine

i. The mid-span deflection of the beam ii. The slope at the left support.

20. A simply supported beam of span 8 m carries two concentrated loads of 20 kN and 30 kN at 3 m and 6 m from left support. Calculate the deflection at the centre by strain energy principle.

21. Using Castigliano’s theorem, determine the deflection of the free end of the cantilever

beam shown in fig. A is fixed and B is free end. Take EI = 4.9 MNm2.

22. The external diameter of a hollow shaft is twice the internal diameter. It is subjected to pure torque and it attains a maximum shear stress ‘τ’. Show that the strain energy stored per unit volume of the shaft is 5 τ2 / 16C. Such a shaft is required to transmit 5400 kw at

110 r.p.m. with uniform torque, the maximum stress not exceeding 84 MN / m2.

Determine,

i. The shaft diameter (8m)

ii. The strain energy stored per m3. Take C = 90 GN / m2. (8m)

23. State and prove Maxwell’s reciprocal theorem.

24. State and prove Castigliano’s theorem.

25. Find the deflection at the mid span of a simply supported beam carrying an UDL of 5 kN/m over the entire span using principle of virtual work. Take span = 5m.


UNIT – II - INDETERMINATE BEAMS

PART – A (2 Marks)

1. A fixed beam of span ‘L’ is subjected to UDL throughout w/m. What is end moments and moment at the centre? (AUC Apr/May 2010)

2. Draw BMD for a propped cantilever beam span ‘L’ subjected to UDL throughout w/m.

(AUC Apr/May 2010)

3. Draw BM Diagram (qualitative) of a propped cantilever of L m long carries an UDL of w/unit run over the entire span. (AUC Nov/Dec 2010)

4. Draw the SF and BM Diagrams (qualitative) of a fixed beam of L m long carries a point load W at the midpoint. (AUC Nov/Dec 2010)

5. What is a fixed beam? (AUC Apr/May 2011)

6. State theorem of three moments. (AUC Apr/May 2011)

7. For the fixed beam shown in fig. what is the fixed end moment at A and B.

clip_image025 (AUC Nov/Dec 2011)

8. For the propped cantilever shown in fig. draw the BMD (qualitative).

clip_image027 (AUC Nov/Dec 2011)

9. Write down the three moment equations for a fixed beam carrying an UDL of 2 kN/m over the entire span. Span = 4m. (AUC Apr/May 2012)

10. State any two methods of analysis of indeterminate beams. (AUC Apr/May 2012)

11. 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.

12. A fixed beam AB of length 3m is having moment of inertia I=3 x 106 mm4 the support B

sinks down by 3mm. If E = 2 x 105 N/mm2. Find the fixing moments.

13. What do you understand by bucking load and safe load?

14. What are the assumptions made in Euler’s theory?

15. What are the fixed end moments for a fixed beam of length l subjected to a concentrated load W at a distance a from left end.

16. State theorem of three moments.

17. What do you mean by a fixed beam?

18. How will you apply clapeyron’s theorem of three moments to a continuous beam with

fixed end supports?

19. Derive a relation fro prop reaction for a simply supported beam with uniformly distributed load and propped t the centre.

20. A Steel fixed beam AB of span 6 m is 60 mm wide and 100 mm deep. The support B

sinks down by 6 mm. Fine the fixing moments at A and B. Take E = 200 GPa.

21. Sketch the bending moment diagram of a cantilever beam subjected o udl over the entire span.

22. What is meant by point of contraflexure?

23. A cantilever beam 4 m long carries a load of 20 kN at its free end. Calculate the shear force and bending moment at the fixed end.

24. What are the advantages and disadvantages of a fixed beam?

25. Define continuous beam?

26. Define flexural rigidity of beams?

27. What is meant by propped cantilever?

28. Write down the general form of clapeyron’s three moment equations for the continuous

beam?

PART – B (16 Marks)

1. For the fixed beam shown in Fig, draw the SFD and BMD. (AUC Apr/May 2010)

2. For the continuous beam shown in Fig, draw SFD and BMD all the supports are at same level. (AUC Apr/May 2010)

3. A fixed beam AB of 4.5m span carries a point load of 80 kN at its mid span and a uniformly distributed load of 15 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. (AUC Nov/Dec 2010)

4. A continuous beam ABCD of uniform cross-section is loaded as shown in Figure Find the following: (AUC Nov/Dec 2010) (i) Bending moments at the supports

(ii) Reactions at the supports.

Also draw BM and SF diagrams.

clip_image033

5. A fixed beam of 6m span is loaded with point loads of 150 kN at distance of 2m from each support. Draw the bending moment diagram and shear force diagram. Also find the maximum deflection. Take E = 200GPa and I = 8 × 108 mm4. (AUC Apr/May 2011)

6. A continuous beam consists of three successive spans of 6 m, 12 m and 4 m and carries loads of 2 kN/m, 1 kN/m and 3 kN/m respectively on the spans. Draw bending moment diagram and shear force diagram for the continuous beam. (AUC Apr/May 2011)

7. A fixed beam AB is 6 m span and carries a point load 10 kN at 1 m from left end. It also carries a clockwise moment at 1 m from right end,10 kN/m. Draw SFD and BMD indicating the salient points. (AUC Nov/Dec 2011)

8. A continuous beam ABCD in shown in Fig. Draw SFD and BMD indicating the salient points. (AUC Nov/Dec 2011)

clip_image035

9. Draw the S.F. and B.M. diagrams for the beam shown in the fig. (AUC Apr/May 2012)

clip_image037

10. Draw the S.F. and B.M. diagrams for the beam shown in the fig. Use three moment equation. (AUC Apr/May 2012)

clip_image039

11. A simply supported beam of span 10m carries a UDL of 1152 N per unit length. The beam is propped at the middle of the span. Find the amount by which the prop should yield, in order to make all the three reactions equal. Take E=2 x 105 N/mm2 and I for beam= 106 mm4.

12. A fixed beam AB of length 6m carries point loads of 160 kN and 120kN at a distance of

2m and 4m from the left end A. Find the fixed end moments and the reactions at the supports. Draw BM and SF diagrams.

13. 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

i. Moments at the supports. (12m)

ii. Deflection at centre of the beam (4m)

Take EI = 15000 kNm2.

12. A cantilever AB of span 6m is fixed at the end ‘A’ and propped at the end B. It carries a point load of 50 kN at the mid span. Level of the prop is the same as that of the fixed end.

i. Determine reaction at the prop. (12m)

ii. Draw the S.F. and B.M. diagrams. (4m)

14. A fixed beam of 6m length is loaded with two equal point loads of 150kN each at distance of 2m from each support. Draw the BMD and SFD. E = 2 x 108 kN/m2, I = 8 x 108 mm4.

15. A continuous beam ABC 8m long consists of two spans AB = 3m and BC = 5m. The span AB carries a load of 50 kN/m while the span BC carries a load of 10 kN/m. Find the support moments and the reactions at the supports.

16. 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 10 kN at a distance of 6m from the left support. Find the fixed end moments and draw the B.M. and S.F. diagrams.

17. A propped cantilever of span of 10m having the prop at the end is subjected two concentrated loads of 15KN and 30KN at one third points respectively from left fixed end support. Draw SFD and BMD.

18. Analyse the following beam.

clip_image041

UNIT – III - COLUMNS PART – A (2 Marks)

1. Define core of a section and draw the same for a circular section. (AUC Apr/May 2010)

2. Write Rankine’s equation for column. (AUC Apr/May 2010)

3. Define: Eccentrically loaded short columns. (AUC Nov/Dec 2010)

4. Distinguish between thick and compound cylinders. (AUC Nov/Dec 2010)

5. How columns are classified depending upon slenderness ratio? (AUC Apr/May 2011)

6. What is thick cylinder? (AUC Apr/May 2011)

7. State any two assumptions made in the derivation of Euler’s formula for long columns. (AUC Nov/Dec 2011)

8. Define ‘core’ of a section. (AUC Nov/Dec 2011)

9. What is the buckling load of an Euler’s column 100mm x 200mm fixed at both the ends

and length is 5m. Take E=200kN/mm2? (AUC Apr/May 2012)

10. Write down the Rankine-Gordon formula. (AUC Apr/May 2012)

11. State middle third rule.

12. How is the failure of thick cylinder different from that of a thin cylinder?

13. Write down the Lame’s equations for thick walled cylinder.

14. What are the advantages of continuous beams over simply supported beams?

15. What are the assumptions made in Euler’s theory?

16. Define slenderness ratio of a column.

17. How the failure of a short and of a long column takes place?

18. How will you determine the hoop stress in a thick compound cylinder?

19. Express the strength of a solid shaft.

20. Differentiate a thin cylinder and a thick cylinder with respect to hoop stress.

21. Discuss the effect of crippling load (Pc) obtained by Euler’s formula on Rankine’s formula for short columns.

22. Give the expression for finding deflection of closely coiled helical spring.

23. Give the equivalent length of a column for any two end conditions.

24. Write down Rankine-Gordon formula for eccentrically loaded columns.

25. Define buckling.

26. Define critical load.

27. What is beam column?

PART – B (16 Marks)

1. i) Derive the Euler’s equation for column with two ends fixed. (AUC Apr/May 2010) ii)A circular bar of uniform section is loaded with a tensile load of 500 kN. The line of action of the load is off the axis of the bar by 10 mm. Determine the diameter of

the rod, if permissible stress of the material of the rod is 140 N / mm2.

(AUC Apr/May 2010)

2. Find the greatest length of a mild steel rod of 30 mm × 30 mm which can be used as a compressive member with one end fixed and the other end hinged. It carries a working

1

load of 40 kN. Factor of safety = 4, α =

clip_image0427500

and σc = 300N / mm2.

Compare the result

with Euler. E = 2 ×105 N / mm2. (AUC Apr/May 2010)

3. i) What are the assumptions and limitations of Euler’s theory for long columns?

ii) A slender pin ended aluminium column 2.0 m long and of circular cross section it to have an outside diameter of 50 mm. Calculate the necessary internal diameter to prevent failure by buckling if the actual load applied is l2kN and the critical load applied is twice the actual load. Take E for aluminium as 70 GN/m2.

(AUC Nov/Dec 2010)

4. i) Describe the Rankine’s method for columns subjected to Eccentricity.

ii) From the following data of a column of circular section calculate the extreme stresses on the column section. Also find the maximum eccentricity in order that there may be no tension anywhere on the section.

External diameter = 20 cm Internal diameter = 6 cm Length of the column = 4 m

Load carried by the column = 175 kN

Eccentricity of the load = 2.5 cm (from the axis of the column) End conditions = Both ends fixed

Young’s modulus = 94 GN/m2. (AUC Nov/Dec 2010)

5. A 1.5m long cast iron column has a circular cross section of 50mm diameter.

One end of the column is fixed in direction and position and the other is free. Taking factor of safety as 3, calculate the safe load using Rankine-Gordon formula. Take yield stress as 560 MPa and constant α = 1/1600. (AUC Apr/May 2011)

6. A pipe of 200mm internal diameter and 50mm thickness carries a fluid at a pressure of

10 MPa. Calculate the maximum and minimum intensities of circumferential stress across the section. Also sketch the radial stress distribution and circumferential stress distribution across the section. (AUC Apr/May 2011)

7. i) A rectangular strut is 25 cm × 15 cm. It carries a load of 60 kN at an eccentricity of 2 cm in a plane bisecting the thickness. Find the minimum and maximum stresses developed in the section.

ii) Derive the Euler’s equation for a long column with both ends hinged.

(AUC Nov/Dec 2011)

8. i) A hollow cylindrical cast iron column is 3.50 long with both ends fixed. Determine the minimum diameter of the column if it has to carry a safe load of 300 kN with a factor of safety 4. External diameter is 1.25 times the internal diameter. a = 1/1600, σc = 550

MN/m2, in Rankine’s formula. (AUC Nov/Dec 2011)

ii) Define ‘thick cylinder’ and draw the hoop stress distribution for a solid circular cylinder.

(AUC Nov/Dec 2011)

9. Derive the expression for the buckling load of an Euler’s column fixed at one end and

hinged at the other end. (AUC Apr/May 2012)

10. A short length of a tube of 60mm external diameter and with thickness 5mm, failed in compression at a load of 250kN. When the same is tested as a strut with both ends hinged 2m long, it failed at a load of 150kN. Find the value of constant ‘α’ in Rankine’s formula. (AUC Apr/May 2012)

11. Derive an expression for crippling load when one end of the column is fixed and the other end is free.

12. Calculate the Euler’s critical load for a strut of T-section. The flange width being 10cm, overall depth 8cm and both flange and stem 1cm thick. The strut is 3m long and is built in at both ends. Take E = 2 x 105 N/mm2.

13. Derive Euler’s crippling load for the following cases:

i. Both ends hinged. (8m)

ii. One end is fixed and other end free (8m)

13. A column with one end hinged and other end fixed has a length of 5m and a hollow circular cross-section of outer dia 100mm and wall thickness 10mm. If E = 1.60 x 105

N/mm2 and crushing stress σc= 350 N/mm2, find the load that the column may carry with

a factor of safety of 2.5 according to Euler theory and Rankine-Gordon theory.

14. i. Derive an expression for the bucking load of a column hinged at both ends. (8m)

ii. A hollow cast iron column whose outside diameter is 200mm has a thickness of

20mm. It is 4.5m long and is fixed at both ends. Calculate the safe load by Rankine- Gordon formula using a factor of safety 4. (8m)

15. A pipe of 200mm internal diameter and 50mm thickness carries a fluid at a pressure of

10 MN/m2. Calculate the maximum and minimum intensities of circumferential stress across the section. Also sketch the radial and circumferential stress distribution across the section.

16. A 2m long pin ended column of square cross section is to be made of wood. Assuming E

=12 GPa and allowable stress being limited to 12 MPa, determine the size of the column to support the following loads safely. (i) 95 KN (ii) 200 KN. Use factor of safety of 3 and also calculates the Euler’s crippling load for buckling.

17. Determine the buckling load for a column of T section with flange of 100mm width and overall depth 120mm. Both flange and web are of 10mm thick. The strut is 3m long with one end hinged and other end fixed.

18. Determine the buckling load for a column of rectangular section of size 100mm width and overall depth 120mm. The strut is 3m long with one end hinged and other end fixed.

19. A compound cylinder is made by shrinking a cylinder of external diameter 300mm and internal diameter 250mm over another cylinder of external diameter 250mm and internal diameter 200mm. The radial pressure at the junction is 8 N/mm2. Find the final stresses set up across the section when the compound cylinder is subjected to an internal pressure of 84.5 N/mm2.

20. i) A hollow mild steel tube 6m long 4 cm internal diameter and 6mm thick is used as a strut with both ends hinged. Find the buckling load and safe load taking factor of safety

3. E = 200 GPa. (8m)

ii) Find the Euler buckling load for a fixed-fixed column. (8m


UNIT – IV - STATE OF STRESS IN THREE DIMENSIONS

PART – A (2 Marks)

1.

Define principal plane and principal stress.

(AUC Apr/May 2010 & Apr/May 2011)

2.

State the principal stress theory of failure.

(AUC Apr/May 2010 & 2012)

3.

Define volumetric strain.

(AUC Nov/Dec 2010)

4.

What are principal stresses and principal planes?

(AUC Nov/Dec 2010)

5.

State distortion energy theory of failure.

(AUC Apr/May 2011)

6.

State the maximum principal stress theory.

(AUC Nov/Dec 2011)

7.

For the state of stress shown in fig. identify the principal planes.

(AUC Nov/Dec 2011)

       

clip_image044

8. What is deviatric component of a stress tensor? (AUC Apr/May 2012)

9. What is meant by stress tensor?

10. State principal strain theory.

11. What will be the fixed end moment for a beam subjected to uniformly varying load, which is maximum at the centre and minimum at supports?

12. State maximum principal strain theory.

13. List the theories of failure.

14. What is stress invariant?

15. What do you mean by triaxial state of stress?

16. What is meant by principal plane?

17. Find the principal stresses if the normal stresses σx and σy and shear stress τ act at a

point?

PART – B (16 Marks)

1. i) Briefly explain spherical and deviatory components of stress tensor. ii) Explain the importance of theories of failure.

iii) For the state of stress shown in Fig, find the principal plane and principal stress.

 (AUC Apr/May 2010)

2. A circular shaft has to take a bending moment of 9000 N/m and torque 6750 N/m. The stress at elastic limit of the material is 207 × 106 N/m2 both in tension and compression. E = 207 x 106 KPa and µ = 0.25.Determine the diameter of the shaft, using octahedral shear stress theory and the maximum shear stress theory. Factor of safety : 2.

(AUC Apr/May 2010)

3. i) State Maximum Shear Stress Theory

ii) A shaft is subjected to a maximum torque of l0 kNm and a maximum of bending moment of 8kNm at a particular section. If the allowable equivalent stress in simple tension is 160MN/m2, find the diameter of the shaft according to the maximum shear stress theory. (AUC Nov/Dec 2010)

4. In a steel member, at a point the major principal stress is 200MN/m2 and the minor principal stress is compressive. If the tensile yield point of the steel is 235MN/m2, find the value of the minor principal stress at which yielding will commence, according to each of the following criteria of failure

i) Maximum shearing stress.

ii) Maximum total strain energy and

iii) Maximum shear strain energy. Take Poisson Ratio = 0.26. (AUC Nov/Dec 2010)

5. The rectangular stress components of a point in three dimensional stress system are

defined as σ x = 20 MPa , σ y = -40 MPa , σ z = 80 MPa ,t xy = 40 MPa ,

t yz = -60 MPa and

t zx = 20 MPa . Determine the principal stresses at the given point. (AUC Apr/May 2011)

6. A steel shaft is subjected to an end thrust producing a stress of 90 MPa and the maximum shearing stress on the surface arising from torsion is 60 MPa. The yield point of the material in simple tension was found to be 300 MPa. Calculate the factor of safety of the shaft according to (i) Maximum shear stress theory and (ii) Maximum distortion energy theory. (AUC Apr/May 2011)

7. i) State the shear strain energy theory and a comment on it.

ii) For the state of stress shown in fig. find the principal plane, principal stress and maximum shear stress. (AUC Nov/Dec 2011)

clip_image048

8. In a material the principal stresses are 50 N/mm2, 40 N/mm2 and – 30 N/mm2. Calculate the total strain energy, volumetric strain energy, shear strain energy and factor of safety on the total strain energy criterion if the material yields at 100 N/mm2.

(AUC Nov/Dec 2011)

9. The state of stress at a point is given by the tensor below. Determine the principal

æ 20 -10 -30 ö

ç ÷

stresses and its directions ç -10 40 20 ÷

è -30 20 -20 ø

MPa. (AUC Apr/May 2012)

10. Explain any two theories of failure. (AUC Apr/May 2012)

11. The normal stress in two mutually perpendicular directions are 600 N/mm2 and 300

N/mm2 both tensile. The complimentary shear stresses in these directions are of intensity

450 N/mm2. Find the normal and tangential stresses in the planes which are equally inclined to the planes carrying the normal stresses mentioned above.

12. A solid circular shaft is subjected to a bending moment of 40 kN m and a torque of 10 kN

m. Design the diameter of the shaft according to i. Maximum principal stress theory

ii. Maximum shear stress theory iii. Maximum strain energy theory.

11. Two mutually perpendicular planes of an element of a material are subjected to direct stresses of 10.5 MN/m2 (tensile); and 3.5 MN/m2 (compressive) and shear stress of 7

MN/m2. Find

i. The magnitude and direction of principal stresses. (12m)

ii. The magnitude of the normal and shear stresses on a plane on which the shear stress is maximum. (4m)

12. Derive the expressions for energy of distortion and energy of dilatation?

æ 9 6 3 ö

ç ÷

13. i. The state of stress at a point is given by ç 6 5 2 ÷ MPa. (8m)

è 3 2 4 ø

ii. Determine the principal stresses. (8m)

14. A cylindrical shell 1.2m diameter is to be made of mild steel plates. It is subjected to an internal pressure of 1.5 MN/m2. If the material yields at 200 kN/m2, calculate the thickness of the plate on the basis of following theories of failure assuming a FOS of 3 in each case.

i. Maximum principal stress theory ii. Maximum shear stress theory

iii. Maximum shear strain energy theory.

15. Determine the principal moments of inertia for an angle section 80 mm x 80 mm x10 mm.

16. Find the principal stresses and principal planes for the following 3D stress field.

æ 10

15

20 ö

σ = ç 15

25

30 ÷ MPa .

ç ÷

è 20 30 40 ø

17. A thick cylinder pressure vessel of inner radius 150mm is subjected to an internal pressure of 80 MPa. Calculate the wall thickness based upon

i. Maximum principal stress theory ii. Total strain energy theory.

Take Poisson’s ratio = 0.3 and yield stress = 300 MPa.


UNIT – V - ADVANCED TOPICS IN BENDING OF BEAMS

PART – A (2 Marks)

1. What is ‘fatigue strength’ and ‘endurance ratio’ in a fatigue testing of material?

(AUC Apr/May 2010)

2. Write the Winkler-Bach formula for a curved beam. (AUC Apr/May 2010)

3. Distinguish between symmetrical and unsymmetrical sections of beams.

(AUC Nov/Dec 2010)

4. What are the causes of fatigue in beams? (AUC Nov/Dec 2010)

5. What are the reasons for unsymmetrical bending? (AUC Apr/May 2011)

6. Write the expression for position of neutral axis in case of curved bars.

(AUC Apr/May 2011)

7. What is stress concentration? (AUC Nov/Dec 2011)

8. For the phase section shown in fig. find the product moment of inertia about x and y

axes. (AUC Nov/Dec 2011)

clip_image050

9. Define: Shear centre. (AUC Apr/May 2012)

10. State Winkler Bach formula. (AUC Apr/May 2012)

11. Define ‘Fatigue’.

12. What are the reasons for unsymmetrical bending?

13. What are the assumptions made in Winkler – Bach theory?

14. What is stress concentration?

15. Define: fatigue life and endurance ratio.

16. How would you find the bending stress in unsymmetrical section?

17. State any four assumptions made in the analysis of stresses in curved bars.

18. When will you use the simple flexure formula for curved beams?

19. What do you mean by unsymmetrical bending?

PART – B (16 Marks)

1. A rectangular simply supported beam is shown in Fig. The plane of loading makes30° with the vertical plane of symmetry. Find the direction of neutral axis and the bending stress at A. (AUC Apr/May 2010)

2. A curved bar of rectangular section, initially unstressed is subjected to bending moment of 2000 N.m tends to straighten the bar. The section is 5 cm wide and 6 cm deep in the plane of bending and the mean radius of curvature is 10 m. find the position of neutral axis and the stress at the inner and outer face. (AUC Apr/May 2010)

3. A thick cylinder of external and internal diameter of 350 mm and 200 mm is subjected to an internal pressure of 45 N/mm2 and external pressure 5N/mm2. Determine the stress in the material. Now if the external pressure is doubled, what internal pressure can be maintained without exceeding the previously determine maximum stress?

(AUC Nov/Dec 2010)

4. Write brief technical note on:

i) Unsymmetrical bending of beams ii) Curved beams

iii) Stress concentration

iv) Significance of shear centre. (AUC Nov/Dec 2010)

5. A 80 × 80 × 10 mm angle is used as a simply supported beam over a span of 2.4m. It carries a load of 400kN along the vertical axis passing through the centroid of the section. Determine the resulting bending stress on the outer corners of the section along the middle section of the beam. (AUC Apr/May 2011)

6. A central horizontal section of hook is a symmetrical trapezium 60 mm deep, the inner width being 60mm and the outer being 30 mm. Estimate the extreme intensities of stress when the hook carries a load of 30 kN, the load line passing 40mm from the inside edge of the section and the centre of curvature being in the load line. (AUC Apr/May 2011)

7. Fig. shows a frame subjected to a load of 3.4 kN find the resultant stress at A and B. (AUC Nov/Dec 2011)

clip_image055

8. A beam of T-section (flange: 100 × 20 mm, web: 150 mm × 10 mm) in 3 m in length and simply supported at ends (Fig). It carries a load of 2.2 kN inclined 20° to the vertical and passing through the centroid of the section. Calculate the maximum tensile stress and maximum compressive stress. Also find the position of the neutral axis. (AUC Nov/Dec 2011)

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9. Determine the shear centre for a channel section shown in fig. (AUC Apr/May 2012)

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10. Find the centroidal principal moments of inertia of an angle section 300mm x 200mm x 20mm as shown in fig. (AUC Apr/May 2012)

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11. A curved bar is formed of a tube of 120 mm outside diameter and 7.5 mm thickness. The centre line of this beam is a circular are of radius 225 mm. A bending moment of 3 kN m tending to increase curvature of the bar is applied. Calculate the maximum tensile and compressive stresses set up in the bar.

12. A 80 mm x 80 mm x 10mm angle section shown in fig is used as a simply supported beam over a span 2.4 m. It carries a load of 400 N along the line YG, where G is the centroid of the section. Calculate the i. Stresses at the points A, B and C of the mid section of the beam

ii. Deflection of the beam at the mid section and its direction with the load line iii. Position of the neutral axis. Take E = 200 GN/m2.

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13. Determine the principal moments of inertia for an angle section 80mm x 80mm x 10mm.

14. A curved bar is formed of a tube of 120mm outside diameter and 7.5mm thickness. The centre line of this beam is a circular arc of radius 225mm. A bending moment of 3 kNm tending to increase curvature of the bar is applied. Calculation the maximum tensile and compressive stresses set up in the bar.

15. A 40mm x 40mm x 5mm angle is used as a simply supported beam over a span of 2.4m. It carries a load of 200N along vertical axis passing through the centroid of the section. Determine the resulting bending stress on the outer corners of the section, along the middle section of the beam.

16. At the critical section of a crane hook, trapezium in section, the inner and outer sides are 4cm and 2.5cm respectively and depth is 7.5cm. The centre of curvature of the section is at a distance of 6cm from the inner fibers. If the maximum stress is not to exceed 120 MN/m2, what maximum load the hook can carry?

17. A curved bar is formed of a tube of 120 mm outside diameter and 7.5 mm thickness. The centre line of this beam is a circular arc of radius 225 mm. A bending moment of 3 kNm tending to increase curvature of the bar is applied. Calculate the maximum tensile and compressive stresses set up in the bar.

18. Determine the horizontal and vertical deflection of the end B of the thin curved beam shown in fig. Take E = 200 GN/m2, width and thickness of the beam 10 mm and 5 mm respectively. P = 2 N.