ce2201 qb2

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SOM-Question Bank-(DSK)

DEPARTMENT OF CIVIL ENGINEERING Question Bank: Strength of Material

UNIT – 1 :- (Simple stresses & strains) 1) Draw the stress-strain curve for tension test on a M.S. specimen

and mark the significant points on it.

2) The Composite bar shown in figure is subjected to a tensile force of 30 KN. The extension observed is 0.372mm. Find the Young Modulus of brass, If Young Modulus of steel is 2 X 105 N/mm2.

P=30KN

300mm400mm

20mm O30mm O

BrassSteel

3) The steel flat shown in figure has uniform thickness of 20mm. Under

an axial load o 80 KN, its extension is found to be 0.17mm. Determine the Young’s Modulus of the material.

Pb1=80mm

b2=40mm

500mm

P=80KN

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4) Find the force P acting at C in the bar as shown in figure. Find the

extension of the bar if E = 2X105 Mpa.

DCBA

P30KN60KN

300mm

15mm=O20mm=O

15mm=O

400mm 300mm

80KN

5) A rigid bar ABCD is connected to steel bar at A and B and is having hinged support at C. At free end a load of 40KN is acting as shown in figure. Find the forces developed in the bars and deflections of free end if E = 2 X 105 N/mm2, diameter of rod at A=30mm and at B is 25mm.

40KN

dCBA

400mm200mm200mm

300mm400mm

6) A steel tube of 50mm outer diameter and 10mm thick is fitted into a

copper tube of inner diameter 50mm and 10mm thick. They are connected by using 20mm diameter pins at the ends. If the length of compound bar is 600mm find the stresses produced in the tubes and pins when temperature is raised by 250C.

Take: αs = 12 x 10-6/0 C, αc = 17.5 x 10-6/0 C, Es = 2 x 105 N/mm2, Ec = 1.2 x 105 N/mm2,


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7) In figure a steel bar of cross-sectional area 250 mm2 held firmly by the end supports and loaded by an axial force of 25KN.

Determine: i) Reactions at L and M. ii) Extension of the left portion.

E=200GN/m2

RM

MNL

0.6m

RL 25KN

30mm O

0.25m

8) For the bar as shown in figure calculate the reaction produced by the

lower support on the bar. Take E = 200GN/m2. Find also the stresses in the bars.

A 1 = 1 10

A 2 = 2 2 05 5 K N

1.2 m m

R 2

N

M

L

2.4

m

1.2m

R 1


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9) The following data relate to a bar subjected to a tensile test:

Diameter of the bar, d = 30mm Tensile load, P = 54KN Gauge length, ℓ = 300mm Extension of the bar, δℓ = 0.112mm Change in diameter, δℓ = 0.00366 Calculate : i) Poisson’s ratio ii) The value of three moduli

10) Composite section made up of copper tube of 150-mm dia enclosed with steel tube 150-mm internal diameter and 12 mm thick. Length of assembly is 50 cm is fastened at both ends. Now temperature of assembly is raised by 75º C. find the stress develop in each material and change in length of assembly. Take Es = 2 x 105 Mpa

Ec = 1 x 105 Mpa


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-: UNIT – 2 :- (Bending Moments & Shear Forces)

1) Draw the shear force and bending diagrams for the beam shown

in figure. Clearly mark the position of the maximum bending moment and determine its value.

x1

150N−m

C B

m 2.0m

2) Draw the B.M. S.F. diagrams for the beam shown in figure

x1

150N−m

C B

m 2.0m

BEAM 3) As shown in figure a beam AB of length 4m acted upon by the

forces and moments. Draw the B.M. and S.F. diagrams

x1

x

150N−m

C B

4.0m 2.0m

300KN

4) A loaded beam as shown in figure, a) sketch the B.M. and S.F. diagrams giving the important numerical values. b) Calculate the maximum bending moment and the point at which it occurs.


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x1

150N−m

C B

4.0m 2.0m

BEAM

5) Draws shear force and bending diagram for the beam shown in figure. Locate point of Contra flexure if any.

6) A beam of span 6m has one support at the left and the other support at a distance of 2m from the right end. The beam carries a UDL of 10kN/m over the entire span. Draw the SFD and BMD and prove that the middle point of the beam is the point of contra flexure.

7) A beam 10 m long has supports at it’s A & B. It carries a point

load of 2.5 KN at 3m from A and a point load of 2.5 KN at 7m from A and a uniformly distributed load of -.5Kn/m between the point loads. Draw the shearing force and bending moment diagrams for the beam.

-: UNIT – 3 (a) :- (Bending Stresses in Beams)

1) Derive the simple bending of a beam formula


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with usual notation. Give the assumption in theory of pure bending. 2) A cast iron water main 12 meters long, of 500mm inside diameter

and 25mm wall thickness runs full of water and is supported at its ends. Calculate the maximum stress in the metal if density of cast iron is 7200kg/m3 and that of water is 1000kg/m3.

Cast iron water main

25mm

500mm

25mm

WATER

3) A hollow circular bar having outside diameter twice the inside diameter is used as a beam. From the bending moment diagram of of the beam, it is found that the bar is subjected to a bending moment of 40KN/m. if the allowable bending stress in the beam is to be limited to 100MN/m2, find the inside diameter of the bar.

4) Two wooden planks 150mm x 50mm each are connected to form a T-section of a beam. If a moment of 3.4 kNm is applied around the horizontal neutral axis, inducing tension below the neutral axis, find the stresses at the extreme fibres of the cross section. Also calculate the total tensile force on the cross-section.

RE

yf

IM

==


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2

1 50mm

150mm

150mm

50mm 5) A beam simply supported at ends and having cross-section as

shown in figure is loaded with a U.D.L., 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 30N/m and in compression to 45MN/m2. What are the actual maximum bending stresses set up in the section.

100mm

30mm

120mm

30mm

120mm

50mm

BEAM

200mm=d

6) A flitched timber beam consists of two joists 100 mm wide and 300

mm deep with a steel plate 200 mm deep and 15 mm thick placed symmetrically in between and clamped to them. Calculate


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the total moment of resistance of the section if the allowable stress in joint is 9MN/m2.

Timber Beam

300mm

100mm15mm100mm

200mm

7) A flitched beam consists of a wooden joist 12cm wide and 20cm deep strengthened by steel plate 1cm thick and 18cm deep, one on either side of the joist. If the stresses in wood and steel are not to exceed 7.5 MN/ m2 and 127.5 MN/ m2 find the moment of resistance of the section of the beam. Take Es = 20 Ew.

Flitched Beam

1.0cm

18cm

1.0cm 12.0 cm

20cm

-: UNIT – 3 (b) :- (Shearing Stresses in Beams)


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1) An I-Section as shown in figure, beam 340 mm x 200 mm has a

web thickness of 10mm and flange thickness of 20 mm. It carries a shearing force of 100 KN. Sketch the shear stress distribution across the section.

340mm=d

BEAM

20mm

200mm

20mm

300mm

T=10mm

Web

Flange

2) A T-shaped cross-section of a beam shown in figure is subjected to

a vertical shear force of 100KN. Calculate the shear stress at the neutral axis and at the junction of the web and the flange. Moment of inertia about the horizontal neutral axis is 0.0001134 m4.

Flange

Web

50mm

200mm

50mm

200mm


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3) A beam of channel section 120mm x 60mm has uniform thickness of 15mm. Draw diagram showing the distribution of shear stress for a vertical section where shearing force is 50KN. Find the ratio between maximum and mean shear stresses.

45mm

Flange

Flange

120mm

Web

T=15mm

90mm

15mm

60mm

15mm

BEAM

4) A steel section shown in figure is subjected to a shear force 200KN.

Determine the shear stress at the important points and sketch the shear distribution diagram.

100mm

Steel Section

300mm

15mm

200mm

300mm


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: UNIT – 5 :- (Deflection of Beams)

1) A steel girder of uniform section, 14 meters long is simply supported at its ends. It carries concentrated loads of 90KN and 60KN at two points 3 meters and 4.5 meters from the two ends respectively. Calculate

i) The deflection of the girder at the points under the two loads

ii) Maximum deflection, Take I = 64 x 10-4 m4 and E = 210x106 KN/m2

x1

150N−m

C

4.0m 2.0m

BEAM

2) A beam AB of 4 meters span is simply supported at the ends and is loaded as shown in figure. Determine

i) Deflection at C ii) Maximum deflection and iii) Slope at the end A Given: E = 200x106 KN/m2 and I = 20x10-6 m4

x1

x

150N−m

C BA

4.0m 2.0m

BEAM


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3) A beam AB as of span 8m is simply supported at the ends A and B and is loaded as shown in figure. If E=200x106 KN/m2 and I=20x10-6m4 Determine

i) deflection at the mid-span ii) maximum deflection iii) slope at the end A

8.0 m

C BA

2.0 m 2.0 m 4.0 m

10KN/m

D

BEAM

4) A beam 6 meters long is loaded as shown in figure. If the flexural rigidity (EI) of the beam is 8x104 KN-m2 find the deflection at point C.

A150N−m

BEAM

300KN

2.0m4.0m

BC

6.0m


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5) A simply supported beam 5m long carries concentrated loads of 10 KN each at points 1 m from the ends.

Calculate: i) maximum slope and deflection of the beam and ii) Slope and deflection under each load Take: EI = 1.2 x 104 KN-m2

E

10KN

C

BA

1.0 m 3.0 m 1.0 m

10KN

D

BEAM

6) A beam 6 meters long is loaded as shown in figure. If the flexural rigidity (EI) of the beam is 8 x 104 KN-m2 find the deflection at point C.

x1

x

150N−m

C BA

4.0m 2.0m

300KN

BEAM


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: UNIT – 6 :- (Principal Stresses and Strains)

1) A rectangular block of material is subjected to a tensile stress of 100 Mpa on one plane and tensile stress of 48 Mpa on a plane at right angles, together with shear stresses of 65 Mpa on the same plane. Find:

i) The magnitude of principle stress. ii) Magnitude of greatest shear stress. iii) The direction of principle plane. iv) The normal and tangential stresses on a plane at 20º

with the plane carrying greater stress.

2) A short metallic column of 500 mm2 cross-sectional area carries an axial compressive load of 100kN. For a plane inclined at 60º with the direction of load calculate: i) Normal stress ii) Tangential stress

iii) Resultant stress iv) Maximum shear stress and v) Obliquity of the resultant stress.

3) The principal stresses at point across two perpendicular planes are 75 MN/m2 (tensile) and 35 MN /m2 (tensile) Find the normal , tangential stresses and the resultant stress and its obliquity on a plane 20º with the major principal plane. 4) At a point in a stressed body the principal stresses are 100 MN/m2 (tensile)and 60 MN/m2 (compressive). Determine the normal stress and the shear stress on a plane inclined at 50º to the axis of major principal stress. Also calculate the maximum shear stress at the point 5) A point is subjected to perpendicular stresses of 50 KN/m2 and both tensile, Calculate the normal tangential stresses and resultant stress and its obliquity on a plane making an angle of 30º with the axis of second stress.

*****END*****


ce2201 qb2

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