Som Tutorials

7/27/2019 Som Tutorials

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TUTORIAL -1STRENGTH OF MATERIAL

Q1. The stress components at a point in a body Subject to two dimensionalstate of stress are given (in kpa)

x = 6x2 + 8xy

y = 3x3 + 4xy2

xy= 6x2y2Determine whether the equations of equilibrium are satisfied at the point(5, 6) or not.

Q.2 The state of stress at a point is given by the following array of terms:

9 6 36 5 2 mpa.

3 2 4

Determine the principal stresses and principle directions.

Q.3 The principal stresses at a point in a body are 60, 50 and -40 Mpa.Calculate the normal and shear stress on the octahedral plane.

Q.4 Compute the stain for the given state of stress in a body.

x = 100 MN /m2 xy = - 500 MN/m

2

y = 50 MN / m2 yz = 50 MN/m

2

z = 200MN/m2- xz = 0 MN/m2

Q.5 Given the following system of strains

x = 5+x2+y2+x4 +y4

y = 6+3x2+3y2 +x4 + y4

xy = 10 + 4xy (x2 + y2 +z)

z = yz = xz = 0Check, whether this system of strain is possible.

Q.6 For the fig. show. Determine the vertical deflection for a load of 10 kg.E = 210,000 N/mm2

Fig


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Q.7 In a material the principle stresses are 60 MN/m2, u and m and -36MN/m2..Calculate.

1. Total strain Energy2. Volumetric strain energy.3. Shear strain energy

4 Factor of safety on the total strain criterion if the material yields, at120 MN /m2

Take E = 200 GN / m2 and = 0.3


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Tutorial 2

Q.1 A beam simply supported at ends and having cross- sectional as shown infig. is loaded with a UDL, over whole of its span. If the beam is 8m long,find the U.D.L. if maximum. Permissible bending stress in tension is

limited to 30 MN/m2 and in compression to 45 MN/m2. What are the actualmaximum bending stresses set up in the section?

Fig

Q.2 A simply supported beam and its cross-section are as shown in fig. Thebeam carries a load W = 20kn as shown. Its self weight is 7 KN/m.Calculate the max normal stress at section 1 1

Fig

Q.3 A wooden beam 15 cm wide and 20 deep is reinforced at the bottom by asteel plate 15 cm wide and 1 cm thick. If the allowable stress in timber is6MN /m2. Find the moment of resistance of the take Es = 15 Ew

Fig

Q.4 A 2 meter long cantilever of rectangular section160 mm wide and 300mm.deep is loaded as shown in fig. Calculate the Deflection at the free end.Take, E = 10.5 GN / m2


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Fig

Q.5 A beam AB of span 8m simply supported at the A and B and is loaded asshown in fig. If E = 200 X 106 and I = 120 X 10-6 m4 determine.

1. Deflection at the mid span.2. Maximum deflection.3. Slope at the end A.

Fig


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Tutorial 3 (Macaulays Method)

Q.1 A beam 4 m span is simply supported at the ends and is loaded as shownin fig. determine.

1. Deflection at C2. Maximum Deflection E = 200 X 106 KN/m2

3. Slope at the end A. I = 20 X 10 -6 m4

Fig

Q.2 Determine the following for an over hanging beam ABC supported at Aand B and loaded as shown.

i) Deflection at the free end Cii) Max. deflection between A and B

Fig

Q.3. A cantilevers beam with a span of 3m carries a point load 30 KN atdistance of 2m from the fixed end. Determine the slope and deflection atthe free end and at the point where load is applied.

MOI = 11924 cm4 & E = 200 GN/m2

Fig

Q.4 A cantilevers 2.5 long is carrying a load of 25 KN at f end and a udl4KN/m. cantilevers is 100 mm wide and 200 mm Find the slope anddefection at the free end A.

E = 2.1 X 10 -8 KN/m2

Fig


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Q.5 A simply supported beam of 4m span is carrying a point load of 40 KN at adistance of 3m from the left end. Calculate the slope at the twosupports and deflection under the load. Also calculate maximumdeflection. EI = 2.6 X 10 7 N-M2

Fig


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Tutorial -4

Q.1 A fixed beam of 6m carries two point loads of 600 KN each at 2m from

each end. Draw the BM and SF diagrams and find the maximumdeflection.Take : E = 2 X 108 KN /m2 and I = 9X108 mm4

Q.2 A fixed beam AB of 5m span is carrying a u d l of 5 KN /m. Find themaximum deflection of the beam.

Q.3 A fixed beam of 6 m span is subjected to a concentrated couple of 150KNm applied at a section 4m from the left end. Find the end momentsfrom the first Principles.

Draw BM and SF. Diagram also.

Q.4 A continuous beam, 12 m long supported over span AB = BC=CD = 4mcarries a uniformly distributed load of 3 KN/m run over span AB aconcentrated load of 4KN at a distance of 1m from point B of supportedBC and a load of 3KN at the centre of the span CD find

i) Support momentsii) Support reactions.Draw the B.M. diagram for the continuous beam.

Q.5 A continuous beam ABC 8m long consists of two spans AB = 3m and BC

= 5m. The span AB carries load of 50 KN/m while the span BC carries aload of 10 KN/m. Findi) Support moment at Bii) Reactions at the supports

Q.6 A continuous beam ABCD, 20m long is loaded as shown in fig. If thesupport B sinks by 10 mm below A and find the support moments.

E = 2.1 X 108 KN/m2

I = 85 X 106 mm4

Fig


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Tutorial 4 (Strength of Material)

Q.1 Calculate the thickness of the metal required for a cast iron main 800mm

in diameter for water at a pressure head of 100m if the max permissibletensile stress is 20 MN/m2. And weights of water are 10 KN / cub m.

Q.2 A cylindrical vessel whose ends are closed by means of rigid flange platesis made of steel plate 3mm thick. The internal length and diameter ofvessel are 50 cm and 25 cm. respectively. Determine the longitudinal andcircumferential stresses in the cylindrical shell due to an internal fluidpressure of 3 MN/m2. Also calculate increase in length, dia and volume ofvessel.

Q.3 To measure the longitudinal and circumferential strains, gauges were fixed

on the outer surface of a closed thick cylinder of diameter ratio. 2.5. At aninternal pressure of 276 MN/m2 these strains were recorded as 11.016 X10-5 and 44.28X10-5 respectively. Determine.

i) Youngs modulesii) Modules of Rigidity

Q.4 Derive the expression for various stresses and show it graphically for thin,thick and compound cylinders.

Q.5 Derive the expression for stress in thick spherical shell.


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TUTORIAL -5

Q.1 Prove that neutral axis the centre of curvature.

Q.2 Derive winkles Bach formula for the curved beams.

Q.3 A curved bar of square section 75X75 mm and of mean radius ofcurvature 115 mm is initially unstressed. The bar is subjected to abending moment of 7500 Nm, which tends to straighten the bar. Findthe stresses at the inner and outer faces and stress distributionacross the section. Also find the position of neutral axis.

Q.4 A crane hook carries a load of 500kg. The line of load being at thehorizontal section through the centre of curvature. The center of

curvature being 40 mm from the same edge. The horizontal section istrapezium whose parallel sides are 14 mm and 26 mm andperpendicular distances are a part 33 mm. Find the greatest tensileand compressive stress in the hook. Also find the position of neutralaxis.

Q.5 A ring made of round steel bar 30 mm diameter and the mean radiusof the ring is 180 mm. Calculate the max tensile and compressivestresses in the material of the ring if it in subjected to a pull of 12KN.


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TUTORIAL 6

Q.1 Find the axial twist, intensity of bending stress and work stored per cm3 inthe spring which is closed coil helical spring made of 12.5 mm diametersteel wire and its ten coils have a mean diameter of 250 mm- If the axialload is 180 N, and axial torque is 14 N-m.

E = 210 X 103 Mpa. G = 84X103 Mpa.

Q2. Show that the shearing stress on the inside of the coil of close coiledhelical spring is larger than that on the out side. Calculate the factor bywhich stress on the inside is higher. Calculate the total stress on the side.

Q.3 An open coiled helical spring is made of 9.525 mm dia steel wire, the coilshaving 14 complete turns and mean diameters of 101.6 mm, the angleof helix being 150 calculate the deflection under 225 N and intensities ofdirect and shearing stresses induced in the section wire. If 225 N axial

load is replaced by an axial torque of 8.5 N-M calculate the angle ofrotation of the coil and the axial deflection. (E = 210 X 10 3Mpa, G = 84X103Mpa)

Q.4 A steel carriage spring is 762 mm in span and carries of 5 KN. The stressis to be limited to 188 Mpa in plates which are 76.5 mm wide and 6.35 mmthick. What will be the stress in any plate and deflection of the spring atthe centre? Also immediately below it and to what radius of curvatureshould each plate be covered.

E = 210 X 103 Mpa.

Q.5 A helical spring has mean diameter of coil of 63.75 mm and consist of 12turns of 6.35 mm diameter wire initially inclination of coil turns is 7 0 .Calculate the axial and angular deformation caused by an axial winding upcouple of 9.06 N-m.

E = 210 X 103 Mpa., G = 84 X 103 Mpa.

Q.6 A flat spiral spring is 6.35 mm wide an 0.25 mm thick The length is 2400mm. Assuming the maximum stress of 0.40 N/mm2 to occur at a sectionwhere BM is greatest, calculate the torque, the energy stored and numberof turns of spindle to wind up full. E = 201 X 103 Mpa.

Q.7 A railway wagon weighing 50 KN and moving with a speed of 8 Kmph onsmooth track has to be stopped by a buffer comprising four springs. Thesprings are identical and each is made of wire of 25 mm diameter woundto a mean radius of coil of 75 mm. Each spring deflects by 220 mm whenwagon strikes against the buffer. Calculate the equivalent graduallyapplied load on each spring, number of turns of each spring and the stressin spring wire.

G = 84 X 102 N/mm2


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TUTORIAL 7

Q. 1 A wooden column of square section is loaded along its axis with.

1. A load of 100 KN with both ends pivoted.2. A load of 200 KN with both ends fixed.3. A load of 150 KN with one end fixed and other pivoted.

The permissible compressive stress of wood is 12 Mpa and its modulus ofelasticity is 12.5 Gpa. Using a factor of safety of 2.5 calculate the size ofcross- section of the column in each case, if length of the column in 2m.

Q.2 A steel rod, rigidly supported at one end is free to expand 1.0 mm beforeit makes contact with the rigid support through a roller attached to rod by apin. What is the minimum temperature rise to cause buckling?

Figure

Q.3 A 1.5 long and 75 mm diameter column of mild steel carries a load of 120KN with eccentricity within 10% of diameters. If the compressive stress isnot to exceed 90 Mpa, check if the column is safe. E = 203 X 103 Mpa.

Assume that the ends of column are pinned.

Q.4 A 4m pivot ended timber column is made of two 50X150mm timbersections nailed together to form a T section. Determine the minimumradius of gyration of cross section and buckling load. E = 12.5 X 10 3 Mpa.

Q.5 A hollow circular aluminum tube 6 m long is used as pivot ended column.Find Euler buckling load of slenderness ration is to be 120.E = 70,00 Mpa. Outer diameter = 150 mm.

Q.6 A 52 mm diameter rod of aluminum alloy is required to carry an eccentricload of 45 KN applied at 20mm from geometric axis. The alloy has anallowable bending stress of 150 Mpa. And its modulus of elasticity is 69X103 Mpa. What is the maximum length of column that can be used safely?


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. TUTORIAL 8

Q.1 A rectangular beam as shown in Fig. is 150 mm wide and 200 mm. deep.It is used as a simply supported beam on a span of 6m. Two loads of 5KN

each are applied to the beam, each load being 2m from a support. Theplane of the loads makes an angle of 30 0 with the vertical plane ofsymmetry. Find the direction of natural axis and the bending stress at thepoint A.

Fig

Q.2 A 20 cm X 20 cm angle is loaded as shown in fig. The total load P being50 KN .Find the direction of the neutral axis between the loads. AlsoCalculate the values of bending Stresses at A, Band C .

Fig

Q.3 A cantilever Beam of I section is used to support the load inclined to the V axis as shown in fig, calculate the stresses at corners A,B,C,&D . Alsolocate the neutral axis.

Fig

Q.4 A 1 beam section is loaded as shown in fig. Determine the stress at A.also locate the position of the neutral axis.


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Fig

Q.5 Determine the shear centre of the channel section. Shown in fig.

Fig

Q.6 Locate the shear centre of the cross section shown in fig.

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