STUPIDSID
Answer any one question from Q1 and Q2
1 (a)
Show that in a bar subjected to sudden loading, the instantaneous stress is twice the stress induced by gradual loading.
8 M
1 (b)
A steel wire 3 m long and 2 mm in diameter is extended by 1 mm when a weight W is suspended from the wire. If the same weight W is suspended from a brass wire 2.5 m long and 2 mm in diameter, it is elongated by 2 mm. Determine the modulus of elasticity of brass if that of steel be 200 Gpa.
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2 (a)
The circular bar as shown in figure 2a is subjected to a tensile load of 60 kN. Find the diameter of middle portion if the stress is limited to 150 MPa, also find length of middle portion if the total elongation of the bar is 0.15 mm, take E = 210 Gpa.
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2 (b)
A steel rod 40mm in diameter is enclosed by a copper tube outer diameter 50mm and inner diameter 40mm. Two pins are fitted transverse at each end to secure the assembly. If the temperature of the assembly is raised through 80°C, calculate the stresses induced in steel rod and copper tube.
For Steal: E= 200 GPa, α=1.2 × 10-5 per °C,
For Copper: E=100 GPa, α=1.8×10-5 per°C.
For Steal: E= 200 GPa, α=1.2 × 10-5 per °C,
For Copper: E=100 GPa, α=1.8×10-5 per°C.
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Answer any one question from Q3 and Q4
3 (a)
A beam ABC with an overhang at one end supports a uniform load of intensity 12 kN/m for 1.6 m length and a concentrated moment of magnitude 3 kN m at C as shown in figure 3a. Draw the shear-force and bending-moment diagrams for this beam.
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3 (b)
The shear-force diagram for a simple beam is shown in the figure 3b. Determine the loading on the beam and draw the bending-moment diagram, assuming that no couples act as loads on the beam.
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4 (a)
A simply supported beam with a span of 4.5 m carries a point load of 30 kN at 3 meters from the left support. If for the section, Ixx = 55×10-6 m4 and E = 200 GPa, find
i) The deflection under the load.
ii) The position and amount of maximum deflection.
i) The deflection under the load.
ii) The position and amount of maximum deflection.
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4 (b)
For the beam and loading shown in Figure 4b, determine the slope at points B and E, Assume E=200 GPa and I=2×108 mm4. Use Macaulay's method.
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Answer any one question from Q5 and Q6
5 (a)
At a point in a strained material, the normal stresses along X and Y direction are 60 MPa tensile and 30 Mpa compressive respectively together with a shear stress of 20 MPa. Using analytical method, determine:
i) Principal stresses
ii) Normal and tangential stresses on a plane inclined at 30° to the plane of 60 Mpa.
i) Principal stresses
ii) Normal and tangential stresses on a plane inclined at 30° to the plane of 60 Mpa.
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5 (b)
For the stress element shown in figure 5b determine the stresses acting on an element oriented at an angle 30° from the x axis. Show these stresses on a sketch of an element oriented at that angle.
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6 (a)
Explain the theory of failure used for brittle material subjected to pure torsion with neat sketch and suitable example.
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6 (b)
A mild steel shaft of 50 mm diameter is subjected to a bending moment of 1.9 kN-m. If the yield point of the steel in simple tension is 200 MN/m2, find the maximum torque that can also be applied according to
i) The maximum shear stress.
ii) The shear strain energy theories of yielding.
i) The maximum shear stress.
ii) The shear strain energy theories of yielding.
10 M
Answer any one question from Q7 and Q8
7 (a)
For the beam and loading shown in Fig 7a, determine the maximum normal stress due to bending.
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7 (b)
A steel bar of solid circular cross section and length L = 2.5 m is subjected to an axial tensile force T = 24 kN and bending moment M = 3.5 kN-m as shown in Fig. 7b. Based upon an allowable stress in tension of, determine the required diameter of the bar; disregard the weight of the bar itself.
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8 (a)
A rectangular beam carries a distributed load of intensity w o on a simply supported span of length L determine critical length at which the shearing stress and flexure stress reach their allowable values simultaneously.
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8 (b)
Fiberglass bracket ABCD of solid circular cross section has the shape and dimensions shown in the figure 8b. A vertical load P=36 N acts at the free end D. Determine the minimum permissible diameter dmin of the bracket if the allowable bending stress in the material is 30 MPa and b=35 mm. (Disregard the weight of the bracket itself.)
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Answer any one question from Q9 and 10
9 (a)
A hollow steel shaft 3 m long transmits a torque of 24 kN-m. The total angle of twist is not to exceed 2.5° and allowable shear stress is 90 Mpa. Find inside and outside diameter of shaft. Take G = 85 Gpa.
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9 (b)
An aluminum bar of 1.2 m length and 30 mm diameter is twisted by torques T acting at the ends. i) Determine the torsional stiffness of the bar, ii) if the angle of twist of the bar is 4°, what is the maximum shear stress? What is the maximum shear strain (in radians)?. Take G = 28 Gpa.
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10 (a)
A 1.5 m long column has a circular cross section of 5 cm diameter. One of the ends of the column is fixed in direction and position and other end is free. Taking factor of safety as 3, calculate the safe load using Rankine's formula and Euler's formula. Take yield stress 560 Mpa, [ alpha = dfrac {1} {1600} ] and E=120 Gpa.
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10 (b)
A horizontal beam AB is pin-supported at end A and carries a load Q at end B, as shown in the figure 10b. The beam is supported at C by a pinned-end column. The column is a solid steel bar (E = 200 Gpa) of square cross section having length L = 1.8 m and side dimensions b = 60 mm. Based upon the critical load of the column, determine the allowable load Q if the factor of safety with respect to buckling is n = 2.0.
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Answer any one question from Q11 and Q12
11
A The U-shaped bar of rectangular cross section is loaded by collinear, oppositely directed forces of 9680 N, as shown in figure 11. The cross- sectional dimensions are 40mm×60mm. The action line of the forces lies 120 mm from the centroid of the cross section. Determine the normal stresses at points A and B.
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12
Consider an initially straight, pin-ended column subject to an axial compressive force applied with known eccentricity e (see figure 12). Determine the maximum compressive stress in the column.
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