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engineering
introduction mechanical engineering

Questions and Answers of Introduction Mechanical Engineering

The state of stress at a point is given by:\[ \sigma_{x}=140 \mathrm{MPa}, \sigma_{y}=100 \mathrm{MPa}, \tau_{x y}=60 \mathrm{MPa} \]Calculate (a) the principal stresses, and (b) the principal
The state of stress at a point is given by\[ \sigma_{x}=300 \mathrm{MPa}, \sigma_{\mathrm{y}}=-200 \mathrm{MPa}, \tau_{x y}=100 \mathrm{MPa}(\mathrm{cw}) \]Draw the Mohr's circle and determine (a)
The state of stress at a point is given by:\[ \sigma_{x}=-150 \mathrm{MPa}, \sigma_{y} 250 \mathrm{MPa}, \tau_{x y}=100 \mathrm{MPa}(\mathrm{ccw}) \]Draw the Mohr's circle and determine (a) the
A rectangular block \(250 \mathrm{~mm} \times 100 \mathrm{~mm} \times 50 \mathrm{~mm}\) is subjected to the following state of stress.\[ \sigma_{x}=100 \mathrm{MPa}, \sigma_{y}=-60 \mathrm{MPa},
A square bar of \(20 \mathrm{~mm}\) side and \(200 \mathrm{~mm}\) long is subjected to a compressive load of 200 \(\mathrm{KN}\) applied in the direction of its length. If all the strains in the
A bar is subjected to the following stresses\[ \sigma_{x}=50 \mathrm{MPa}, \sigma_{y}=-40 \mathrm{MPa}, \sigma_{z}=70 \mathrm{MPa} \]If \(v=0.25\) and \(E=200 \mathrm{GPa}\), calculate (a) the
The following strains were measured on pressures vessel\[ \varepsilon_{x}=500 \times 10^{-6}, \varepsilon_{y}=-100 \times 10^{-6} \]and at \(45^{\circ}\) with \(x\)-axis, \(\varepsilon_{z}=-200
The state of strain at a point is given by\[ \varepsilon_{x}=400 \times 10^{-6}, \varepsilon_{y}=-200 \times 10^{-6}, \gamma_{x y}=250 \times 10^{-6} \]Calculate (a) the principal strains, and (b)
The principal strains at a point are given by\[ \varepsilon_{1}=800 \times 10^{-6}, \varepsilon_{2}=-600 \times 10^{-6}, \varepsilon_{3}=400 \times 10^{-6} \]If \(v=0.25\) and \(\mathrm{E}=200
A circle \(50 \mathrm{~mm}\) in diameter is scribed on a mild steel plate before it is subjected to the following state of stress:\(\sigma_{x}=200 \mathrm{MPa}, \sigma_{y}=100 \mathrm{MPa}=\tau x
Define a beam.
Define sagging and hogging bending moment.
Define point of inflation.
Define point of ontraflexure.
Explain the sign convention for shear force.
What is the solution ship between load, shear force and bending moment?
Draw the shear force and bending moment diagrams for the simply supported beam loaded as show in Fig. 15.34. 20kN/m A 2m 15kN 1.5m D 3m Fig. 15.34 10kN E B 1.5m-
Draw the B.M. and S.F. diagrams for the simply supported beam loaded as shown in Fig 15.35 . 20kN A 1.5m B 3m 30kN -10kN/m + Fig. 15.35 3m D 15kN E 2m
Draw the B.M. and S.F. diagrams for the simply supported beam loaded as shown in Fig. 15.36. 15kN 20kN/m 1m B 1.5m Fig. 15.36 2.5m D 50kN/m
Draw the B.M. and S.F. diagrams for the beam loaded as shown in Fig. 15.37 . A 15kN/m B 3m Fig. 15.37 1.5m 150kN.m 1.5m D
Draw the B.M. and S.F. diagrams for the beam shown in Fig. 15.38 . 10kN 100 kNm 20kN 2m B 2m Fig. 15.38 2m D 2m E
Calculate the value of ‘a’ so that maximum positive bending moment is equal to the maximum negative bending moment for the beam shown in Fig. 15.39 B w/unit length Fig. 15.39
Draw the B.M. and S.F. diagrams for the beam shown in Fig. 15.40. 50kN/m 2m 4m B 50kN T 1m Fig. 15.40 2m D 2m 150kN E
Draw the B.M. and S.F. diagrams for the beam shown in Fig 15.41 20kN.m B 11 1m 3m 1m Fig. 15.41 20kN.m
Draw the bending moment and shear force diagrams for the simply supported beam loaded as shown in Fig. 15.16 (a). RA 2m 5kN 6kN 4kN to 2m 2m 15.5 (a) 21 A C 7.75 + 2.75 + D (b) B.M.D. A C D 3.25 E
Drawn the bending moment and shear force diagrams for the simply supported beam shown in Fig 15.17 (a).
Draw the B.M. and S.F. diagrams for the simply supported beam shown in Fig. 15.18 (a). A C 10kN D 1m- |1m| x (a) 3m E 10.833 11.866 !12.499 13.332 x 1mm B 6.665 kN.m A C D E B (b) B.M.D.
Drawn the B.M. and S.F. diagrams for the cantilever beam shown in Fig 15.19 (a). x -5kN/m 3m x (a) 2m 10kN B
Draw the B.M. and S.F. diagrams for the cantilever beam shown in Fig. 15.20 (a) 5kN T 5kN A 1m C 1m-> D 3m B (a)
Draw the B.M. and S.F. diagrams for the overhanging beam shown in Fig. 15.21 (a) 5kN 3kN B C 1m- 1m- 2m RB B A 5 5 1 (a) (b) B.M.D. 6kN 4KN D E F D 1m - RB E 4kN.m 'F B C D (c) S.F.D. 10 5
Draw the B.M and S.F. diagrams for the beam shown in Fig. 15.22 (a)
Draw the B.M. and S.F. diagrams for the beam shown in Fig 15.23 (a).
Draw the B.M. and S.F. diagrams for the beam shown in Fig 15.24 (a).
Draw the B.M. and S.F. diagrams for the beam shown in Fig. 15.25 (a). A RA 5kN 1m 3m (a) 9kN D 1m B RA
A beam is loaded as shown in Fig 15.26 (a). Draw the B.M. and S.F.diagrams.
A cantilever beam is loaded as shown in Fig 15.27(a). Draw the B.M. and S.F. diagrams. A 20kN/m 4m (a) B 25kN C 1m-
A cantilever beam is loaded as shown in Fig. 15.28 (a). Draw the B.M. and S.F. diagrams. 15kN 10kN A 5m (a) B 2m.
Draw the B.M and S.F. Diagrams for the beam loaded as shown in Fig 15.29.
Draw S.F. and B.M. Diagrams for the beam shown in Fig 15.30 Find the position and magnitude of bending moment and the points of contraflexure. 40kN 50kN/m 60kN 000 D B 5m 2m- A 1.5m Fig. 15.30
A simply supported beam with overhanging ends carries transverse loads as shown in Fig. 15.32 (a) If W = 10 w, what is the overhanging length on each side such that bending noment at middle of beam
A beam AB, 10m long is carrying a uniformly distributed load of intensity w N/m. The beam is to simply supported on two supports 6m apart in such a way that the bending moment on the beam is as small
At the neutral axis of a beam(a) bending stress is zero(b) bending stress is maximum(c) shear force is zero(d) shear force is maximum
In a beam subjected to simple bending, the bending stress is(a) directly proportional to the distance from the neutral axis(b) inversely proportional to the distance from the neutral axis(c) directly
In the simple bending of beam theory, the plane of leads(a) does not coincide with the centroidal plane(b) coincides with the centroidal plane(c) is inclined at \(45^{\circ}\) to the centroidal
In the simple bending of beams, the bending stress is the beam varies(a) linearly(b) parabolically(c) hyperbolically(d) elliptically
the moment of resistance \(\left(m_{r}\right)\) of a beam is(a) directly proportional to the section modules ( \(\mathrm{z}\) ) of the beam(b) \(m_{r} \times \frac{1}{z}\)(c) \(m_{r} \times
The top fibres of a cantilever beam carrying end load develope(a) compressive stress(b) tensile stress(c) strear stress(d) bending stress
The shear stress in a circular shaft under torsion varies(a) uniformly(b) lineraly (c) parabolically (d) hyperbolically
The maximum shear stress in a shaft under torsion occurs at the(a) centre of shaft(b) outermost fibres(c) mid-radius(d) square root of radius
The torsional rigidity of a shaft is given by(a) \(\frac{T}{J}\)(b) \(\frac{T}{r}\)(c) \(\frac{T}{\theta}\)(d) \(\frac{T}{l}\)
The torsional section modules of a circular shaft is(a) \(\frac{J}{\theta}\)(b) \(\frac{J}{l}\)(c) \(\frac{J}{r}\)(d) \(\frac{T}{G}\)
State parallel axis theorem.
What is neutral axis.
State the assumptions made in simple bending theory.
Define section modulus.
Define bending stiffness
What is moment of resistance ?
What are the assumptions made in deriving the torsion formula ?
Define torsional stiffness.
Define torsional section modulus.
White the torsion formula and give S.I. units of various terms.
An inverted \(T\)-beam of \(4 \mathrm{~m}\) span is simply supported at the ends. Its cross-section is 300 \(\mathrm{mm} \times 250 \mathrm{~mm} \times 10 \mathrm{~mm}\). If permissible stresses in
A rolled steel joist \(400 \mathrm{~mm} \times 200 \mathrm{~mm} \times 20 \mathrm{~mm}\) is freely supported on a span of \(4 \mathrm{~m}\). The flanges are strengthened by two \(250 \mathrm{~mm}
A rectangular cross-section beam has a width of \(100 \mathrm{~mm}\). Determine the depth of the beam so that maximum bending stress in the beam does not exceed \(35 \mathrm{MPa}\). The maximum
A cast iron water main pipe \(12 \mathrm{~m}\) long, \(500 \mathrm{~mm}\) inside diameter and \(25 \mathrm{~mm}\) wall thickness runs full of water. It is supported at its ends. If the density of
A uniform heavy girder of length \(10 \mathrm{~m}\) is to be placed over two supports \(6 \mathrm{~m}\) apart. Calculate the length of overhang for the girder at both ends so that the maximum bending
A solid steel shaft is required to transmit \(45 \mathrm{~kW}\) at \(150 \mathrm{rpm}\). If the permissible shear stress is \(75 \mathrm{MPa}\), find the diameter of the shaft.
A shaft is required to transmit \(7.5 \mathrm{~kW}\) at \(600 \mathrm{rpm}\). The maximum torque exceeds the mean torque by \(40 \%\). Calculate the diameter of the shaft if shear stress is not to
A hollow steel shaft of external diameter \(400 \mathrm{~mm}\) and metal thichness \(25 \mathrm{~mm}\) is required to transmit power at \(240 \mathrm{rpm}\). If the shear stress is not to exceed \(63
A solid shaft of \(100 \mathrm{~mm}\) diameter is to be replaced by a hollow shaft with internal diameter equal to \(40 \%\) of external diameter. Find the size of hollow shaft and saving in
The cross-section of a T-section beam is shown in Fig. 16.8 (a). It is subjected to a bending moment of 1.5 kNm. Plot the distribution of stress due to bending in the beam. N- y 30 10 A 30mm (a)
The cross-section of an I-beam is shown in Fig. 16.9. The bending moment at the section is 20 kN.m. Plot the distribution of bending stress in the beam. N- 8- 120 10 10 -56.92 150- (a) I-section
A cast iron channel carries water as shown in Fig. 16.10. It is supported at two points 12 m apart. Density of water is 1000 kg/m3 and that of cast iron 7000 kg/m3. Calculate the depth of water in
A cantilever beam with triangular cross-section as shown in Fig. 16.11 carries a uniformly distributed load of intensity 2 kN/m over its entire length. If the depth h = 2b, determine the minimum
A timber beam as shown in Fig. 16.12 is simply supported on a span of 4 m.The weight of the beam is 10 kN/m3 and the permissible stress in timber is 10 MPa. Calculate the safe point load at mid-span.
A beam of 3 m length is simply supported at the ends and carries a uniformly distributed load of 40 kN/m over its whole span. The cross-section of the beam is shown in Fig.16.13. Calculate the
A log of timber 300 mm in diameter is available to be used as a beam.Calculate the following:(a) Dimensions of the strongest rectangular section that can be cut out of it.(b) Maximum span to carry a
A beam of I-section shown in Fig. 16.15 is subjected to be bending moment of 12 kN.m. Find the maximum tensile and compressive stresses induced in the beam. N-T y 1) 3 -50- 15 (2 20 T -A 150mm 100
A hollow shaft of diameter ratio 0.6 is required to transmit 500 kW at 100 rpm. The maximum torque being 15% greater than the mean. The shear stress is not to exceed 60 MPa and the angle of twist in
Compare the weights of two solid shafts of identical length, one of steel and the other of aluminium alloy, both designed for the same angle of twist per unit length when subjected to the same
A solid aluminium shaft 1m long and 45 mm outside diameter is to be replaced by a tubular steel shaft of the same length and the same outside diameter so that either shaft could carry the same torque
A solid shaft is to transmit 300 kW at 80 rpm. The shear stress is not to exceed 60 MPa. Find the shaft diameter. Calculate the percentage saving in weight if this shaft were replaced by a hollow one
A hollow shaft of diameter ratio 0.6 is required to transmit 450 kW at 100 rpm, the maximum torque being 20 % greater than the mean value. The shear stress is not to exceed 56 MPa and the angle of
A solid circular shaft is to transmit 250 kW at 120 rpm. (a) If shear stress is not the exceed 63 MPa, find its diameter. (b) If this shaft is replaced by a hollow shaft whose diameter ratio is 0.6,
A hollow steel shaft is to be replaced by an aluminium shaft of the same external diameter. The material of steel shaft is 25% stronger than aluminium shaft in shear.Calculate the diameter ratios.
A solid shaft of medium carbon steel 100 mm diameter is to be replaced by a hollow shaft of alloy steel. The shear strength of alloy steel is 30% greater than medium carbon steel. The power to be
The principal stresses at a point in a piece of material are \(90 \mathrm{MPa}\) tensile and \(60 \mathrm{MPa}\) compressive. Find the intensity and direction of the stress across a plane the normal
At a point in a piece of material the intensity of resultant stress on a certain plane is \(50 \mathrm{Mpa}\) inclined at \(30^{\circ}\) to normal to that plane. The plane normal to this has a
At a point in a material subjected to two direct stresses on planes at right angles, the resultant stress on a plane \(A\) is \(80 \mathrm{MPa}\) inclined at \(30^{\circ}\) to the normal, and on
The principal stresses at a point in a material are \(120 \mathrm{MPa}\) and \(60 \mathrm{Mpa}\). Find the magnitude and direction of stress on a plane inclined at \(30^{\circ}\) to the direction of
The state of stress at a point is given by:\[ \sigma_{x}=60 M P a, \sigma_{\mathrm{y}}=-30 M P a, \tau_{\mathrm{xy}}=30 M p a(c c w) \]Calculate (a) principal stresses, (b) principal planes, (c)
At a point in a load carrying member, the state of stress is as given below.\[ \sigma_{x}=400 \mathrm{MPa}, \sigma_{\mathrm{y}}=-300 \mathrm{MPa}, \tau_{\mathrm{xy}}=200 \mathrm{MPa}(\mathrm{ccw})
. The state of stress at a point is given by\[ \sigma_{x}=-120 \mathrm{MPa}, \sigma_{\mathrm{y}}=180 \mathrm{MPa}, \sigma_{\mathrm{xy}}=80 \mathrm{MPa}(\mathrm{ccw}) \]Draw the Mohr's circle the
The principal stresses at a point in a stressed body are \(20 \mathrm{MPa}\) and \(8 \mathrm{MPa}\). Determine the maximum obliquity of the resultant stress P Omax A B = 20MPa Fig. 14.16 x + y 2 =
The state of stress at a point is given by:\[ \sigma_{x}=400 \mathrm{MPa}, \sigma_{y}=200 \mathrm{MPa}, \tau_{x y}=100 \mathrm{MPa}(\mathrm{ccw}) \]Calculate the normal, shear and resultant
The normal stresses on two neutrally perpendicular planes are \(100 \mathrm{MPa}\) (tensile) and \(40 \mathrm{MPa}\) (compressive) together with shear stress of \(70 \mathrm{MPa}\). Determine
: A bar of \(20 \mathrm{~mm}\) diameter is subjected to a pull of \(20 \mathrm{kN}\). The measured extension over a gauge length of \(200 \mathrm{~mm}\) is \(0.1 \mathrm{~mm}\) and the change in
A material is subjected to two mutually perpendicular linear strains together with a shear strain. One of the linear strain is \(250 \times 10^{-6}\) tensile. Determine the magnitude of the other
A circle of \(100 \mathrm{~mm}\) diameter is scribed on an aluminium plate before it is loaded as shown in Fig. 14.30. After stressing the circle deforms into an ellipse. Determine the lengths of
Justify the necessity for NC machines.

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