B.TECH - Semester 3 mechanics of structures Question Paper 2021 (may)
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- Direct stresses of $120 \mathrm{MN} \mathrm{m}^{2}$ in tension and $90 \mathrm{MN} / \mathrm{m}^{2}$ m in compression are applied lo an elastic malerial al a certain poinl on planes al right angles lo each other. (c) Find the magnitude of the olner principal stress and its mclinalion to $120 \mathrm...
- (a) Analyse the gin foinled frame shown in Fig. 2 and find out the member forces,
- (a) A 3 m long bar, circular in section is having uniorm diameler of 20 mm for a length of 1.5 m . In the next 0.5 m , its diameter gradually increases to "d mm and for the remaining 1 m , the diameler " $d$ " remains the same. When a lensile load of 200 kN is applied al the ends of the bar, the ext...
- (b) A bar made or brass and steel as shown in Fig, 1 is held between two rigid supports at A and C . Find the stress in each partion if the temperalure rises by $40^{\circ} \mathrm{C}, E_{b}=1 \times 10^{5} \mathrm{MPa}, E_{s}=2 \times 10^{5} \mathrm{MPa}, \alpha_{b}=19 \times 10^{-4} \mathrm{f}^{\c...
- (b) Draw the bending moment diagram and shear force diagram for the simply supported beam in Fig. 3. Figure 3 12 (a) Calculate the dimensions of the strongest reclangular seclion that can be cut out of a circular log of wood 25 cm diameter.
- (b) Also specify the sale maximum span for this beam of reclangular section for carrying a UDL of $2.5 \mathrm{kN} / \mathrm{m}$ and to limil the bending stress to $10 \mathrm{MN} / \mathrm{m}^{2} . \quad 5$
- (c) What will be the Iongest span, it the circular log ilsell is used as a beam?
- (a) A short column of hollow cylindrical section 25 cm outer diameter and 15 cm inner diameler carries a verlical load of 400 kN along one of the diameler planes 10 cm away from the axis of the column. Find the maximum and minimum inlensilies of stresses and slate theft nalure.
- (b) A thick steel cylinder having internal diameter 100 mm and exlernal diameter 200 mm is subjected lo an internal pressure oi 55 MPa and external pressure of 7 MPa . Find the maximum hoop stress, OR
- (a) Find the maximum lorque that can be salely applied to a shaft of 100 mm diameter. The permissible shear stress and the allowable twist are respectively $200 \mathrm{~N} / \mathrm{mm}^{2}$ and $3^{2}$ per 10 diameter length of the shaft. Take modulus of rigidity as $1 \times 10^{5} \mathrm{~N} / ...
- (b) Waler under a pressure of $8 \mathrm{~N} / \mathrm{mm}^{2}$ is suddenly admilled on a plunger of 100 mm diameler allached lo a rod of 32 mm diameler and 12 mlong . Find the maximum instanlaneous stress and deformalion of the rod. Take modulus of elaslicily (E) as $2 \times 10^{5} \mathrm{~N} / \...
- List the assumptions used in the theory of simple bending,
- Explain how principal stresses are evaluated using Morh's circle method, for a body subjected to biaxial direct stresses and shear stress.
- Derive the relation between rate of loading, shear force and bending momenl.
- Explain kern of a section and locale the kern of a circular section.
- Draw the shear stress distribution along the depth of a reclangular beam of size 200 mm wide and 350 mm deep, if the section is subjected to a shear force of 30 kN . Also find out the maximum shear stress.
- Proportion a simply supported team of unform strength having a span of 4 m subjected to a central poinl load of 10 kN by keeping a conslanl width of 100 mm ,
- Differentiate between thin and thick cylinders. List the various types of stresses in these cylinders.
- Derive the relation between torsional moment, angle of twist and shear slress for a circular shall subjected lo lorsion. $$ \{\theta \times 5=40 \text { Marks }\} $$
- Direct stresses of $120 \mathrm{MN} \mathrm{m}^{2}$ in tension and $90 \mathrm{MN} / \mathrm{m}^{2}$ m in compression are applied lo an elastic malerial al a certain poinl on planes al right angles lo each other. (a) If the maximum principal sliess is nol to exceed 150 Milim $^{2}$ in tension, to wh...
- Direct stresses of $120 \mathrm{MN} \mathrm{m}^{2}$ in tension and $90 \mathrm{MN} / \mathrm{m}^{2}$ m in compression are applied lo an elastic malerial al a certain poinl on planes al right angles lo each other. (b) In this condilion, what is the maximum shear stress in the material?
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