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PVP SIDDHARTHA INSTITUTE OF TECHNOLOGY, KANURU MECHANICAL ENGINEERING DEPARTMENT II.B.TECG SECTION-I MOS M OS A SSI G NM E NT -1
1. a) A steel wire 2m long and 3mm in diameter is extended by 0.75 mm when a weight ‘w’ is suspended from the wire. If the same weight is suspended from a brass wire, 2.5m long and 2mm in diameter, it is elongated by 4.64 mm. Determine the modulus of elasticity of brass if that of steel be 2 × 105 N/mm2. b) A Concrete column of cross-Sectional area 400mm × 400mm is rein forced by four longitudinal 50mm diameter round steel bars placed at each corner. If the column carries a compressive load of 300kN, determine i) The compressive stress produced in the concrete and steel bars ii) Loads carried Young’s Modulus of elasticity of steel is 15 times times that of concrete. 2.
A circular circular steel steel bar ABCD, rigidly rigidly fixed fixed at A and D is is subjected subjected to axial loads of 50 KN and 100 KN at ‘B’ and ‘C’ as shown in the figure. Find the loads shared by each part of the bar and the displacements of the points ‘B’ and ‘C’. The value of young’s Modulus for steel is 200 Gpa.
3.
A steel steel rod rod 28 mm diameter diameter is is fixed fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. (a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm. (b) Find the increase in the distance between the stops if the force exerted between them is 90 kN Take ES = 200kN/mm2 ; αS = 11.2 × 10−6 per 0C E b = 90kN/mm2 ; α b = 2.1 × 10−5 per 0C
4. (a) Draw stress-strain diagram for mild steel specimen tested under uni-axial tension till fracture and mark all the salient points. (b) A metallic rod of 1 cm diameter, when tested under an axial pull of 10 kN was found to reduce its diameter by 0.0003 cm. The modulus of rigidity for the rod is 51 kN/mm2. Find the Poisson’s ratio and Modulus of elasticity. 5. The truss ABC shown in figure supports at joint B a force P that acts at angle θ to the vertical. The cross-sectional areas and moduli of elasticity of members AB and BC are same. Find the angle θ so that the deflection of joint B will be in the same direction as the force P.
6. A rigid bar of AB of length L is hinged to a wall at A and supported by two vertical wires attached at a points C and D (see figure). The wires have the same cross-sectional areas and are made of the same material, but the wire at D is twice as long as the wire at C. Find the tensile forces Tc and Td in the wires due the vertical load P acting at end B.
PVP SIDDHARTHA INSTITUTE OF TECHNOLOGY, KANURU MECHANICAL ENGINEERING DEPARTMENT II.B.TECH SECTION-I & II MOS ASSI G NM E NT -2
1.
a) Determine an expressions which relates Young’s Modulus, Modulus of Rigidity and Bulk Modulus. b) A Metallic bar 250mm x100mm x 50mm is loaded as shown in figure. Find the change in volume. Take E=2x105 Mpa and Poisson’s ratio=0.25. Also find the change that should be made in the 4MN load, in order that there should be no change in the volume of the bar.
2.
a) Calculate the Modulus of Rigidity and Bulk Modulus of a cylindrical bar of diameter of 25mm and length 1.6m, if the longitudinal strain in a bar during a tensile test is four times the lateral strain. Find the change in Volume, when the bar is subjected to a hydrostatic pressure of 100Mpa. Take E=1x10 5 Mpa. b) Determine an expression for volumetric strain of a rectangular bar subjected to three forces which are Mutually Perpendicular.
3.
A 10 mm diameter rod was subjected to an axial pull of 10 kN and the change in diameter was observed to be 0.003 mm. Calculate Poisson’s ratio and modulus of elasticity. Find also bulk modulus. Given rigidity modulus = 5×104 N/mm2.
4.
(a) Define statically determinate and statically indeterminate beams. Give examples. (b) A cantilever beam of length 2m carries a uniformly distributed load of 2 kN/m over the whole length and a point load of 3 kN at the free end. Draw the SF and BM diagrams.
5.
A 10m long simply supported beam carries a point load of 4kN at 8m from the left end along with a uniformly distributed load of 4kN/m intensity for 3m length starting from the left end. The beam is also acted upon by a clockwise couple of 10kN.m at midpoint of the span. Draw the shear force and bending moment diagrams.
6.
a) Draw the SF and BM diagrams for the cantilever loaded as shown in the figure.
b) Draw the SF and BM diagrams for the simply supported beam shown in the fi gure.
PVP SIDDHARTHA INSTITUTE OF TECHNOLOGY, KANURU MECHANICAL ENGINEERING DEPARTMENT II.B.TECH SECTION-I & II
Assignment-III MOS-I (2013-14) 1. A beam of square section of the side ‘a’. If the possible bending stress is ‘σ’ find the moment of the resistance when the beam is placed i.e. (i) Two sides are horizontal. (ii) One diagonal is vertical. Find also the ratio of the moment of resistance of the section in the two positions. 2. A timber beam 100mm wide and 200mm deep is to be reinforced by bolting on 2 steel fitches each 150mm by 12.5mm in section .calculating the moment of resistance in the following cases. (i) Fitches attached symmetrically at the top and bottom. (ii) Fitches attached symmetrically at the sides allowable stress in timber is 6 N/2.what is the maximum stress in the steel in each case take =2×106 / 2 . =1×104 /2. 3. Two rectangular plates one of the steel and other of brass each 40mm wide and 100mm deep are placed together to form a beam 40mm wide and 20mm deep on two support 1m apart, the brass plate being on the top of the steel plate. Determine the maximum load which can be applied at the centre of the beam. If the plates are (i) Separate 4 can bend independently. (ii) Firmly secured throughout their length. Maximum allowable stress in steel =112.5 N/2 . And in brass =75 N/2 .Take =2×105 / 2 And =8×104 N/2 . 4. A beam of square section is used a beam width 1 diagonal horizontal .the beam is subjected to a shear force ‘F’ at a section. Find the maximum shear in the cross sectional of the beam and draw the shear distribution diagram for the section. 5. For the section shown in fig.5, determine the average shear stress at A,B,C and D for a shearing force & 20kw.draw also the shear stress distribution diagram.
