1.a. Briefly explain the principles of limit state.

1.b. Briefly explain the modes of failure of beam sections with sketches.

1.c. What are the causes of cracking in RC members?

2.a. 2 A simply supported beam has a rectangular section and carries a uniformly distributed load of 20 kN/m over a clear span of 4.5 m. The cross section is 330 mm $\times$ 550 mm and is reinforced with 4 no’s of 20 mm diameter bar.

Assume cover = 25 mm and bearing = 300 mm. Assuming, M20 grade concrete and Fe415 steel, compute short and long term deflection of the beam.

3.a. A Cantilever R.C. beam of span 2 m is rectangular in cross section 230 mm $\times$ 380 mm. It is reinforced with 3 – 16 mm diameter bars on tension side.

Assume clear cover as 25 mm. M20 grade concrete and Fe415 steel is used. Determine the permissible concentrated load at the free end of Cantilever.

3.b. A Doubly reinforced beam section 250 mm wide 500 mm deep to the centre of the tensile reinforcement. It is reinforced with 3 – 16 mm diameter bars as compression reinforcement at an effective cover of 50 mm and 4 bars of 20 mm diameter as tension reinforcement. Determine the moment of resistance of the section. M20 concrete and Fe500 steel is used.

4.a. Determine the minimum effective depth required and the corresponding area of tension reinforcement for a rectangle beam having a width of 200 mm to resist an ultimate moment of 200 kN-m. M20 grade concrete and Fe415 steel is used.

4.b. A reinforced concrete beam has a support section with a width of 250 mm and effective depth of 500 mm. The support section is reinforced with 3 bars of 20 mm diameter on the tension side. 2 legged 8 mm diameter stirrups are provided at a spacing of 200 mm centre to centre. Calculate the shear strength of the support section for M20 grade concrete and Fe415 steel.

4.c. A singly reinforced slab 120 mm thick is supported by T-beam spaced at 3 m C/C, the effective depth and width of web are 580 mm and 450 mm respectively. Eight HYSD bars of 20 mm diameter have been provided in tension in two layers, with 4 no’s in each layer. The effective cover in lower tier is 50 mm. The effective span of simply supported beam is 3.6 m and grade of concrete is M20. Determine the depth of neutral axis and the moment of resistance of T-beams section.

5.a. Design the shear reinforcement for an RC beam 300 mm $\times$ 600 mm effective carrying a uniformly distributed load of 30 kN/m run factored over a span of 6 m supported over 300 mm wide beams. Use M20 grade concrete and Fe415 grade steel.

5.b. Design the reinforcement for tension and compression reinforcement side and its percentage for a doubly reinforced rectangular beam simply supported at both ends. The size of the beam is 300 mm $\times$ 600mm effective. Effective cover to compression reinforcement is 50 mm. The ultimate factored total load of 90 kN/m including self weight of beam is acting between the supports of effective span 6.0 m. Grade of concrete and steel are M20 and Fe415.

6.a Design one of the intermidate T-beam for a hall measuring 7 m $ \times$ 12 m with beams spaced at 3 m C/C. Depth of slab is 120 mm. Live load on slab is $9.5 kN/m^2$ including finishes. Use M20 grade concrete and HYSD bars.

7.a. Distinguish between one way and two way slab.

7.b. Design an interior panel of a two-way slab of size 5m $\times$ 5m . Live load = $3 kN/m^2$, floor finish = $1 kN/m^2$ and bearing = 300 mm. Adopt M20 grade concrete and Fe415 grade steel. Sketch the reinforcement details in plan.

8.a. The clear dimension of a stair case hall is 2.4 m $\times$ 4.75 m. The floor to floor height is 3.52 m. A two flight dog legged stair is to be provided between the two floors with a rise of 160 mm. Design the stairs and also check for deflection. Sketch the reinforcement details of any one of the flight.

9.a A RCC square column of side 300 mm is reinforced with 4 bars of 16 mm diameter. Determine the allowable service load on the column. M25 grade concrete and Fe500 steel is used.

9.b. A rectangular column of size 300mm $\times$ 500mm is subjected to an axial load of 1200 kN and moment of 30 kN-m acting about an axis bisecting the depth of column.

Effective cover = 50 mm. Calculate the necessary reinforcement adopting M20 grade concrete and Fe415 steel. Sketch the reinforcement details

10.a Design a rectangular footing of flat type for a column of size 300 mm$\times$ 500 mm carrying an axial load of 1200 kN. SBC of soil is 200 $kN/m^2$. Adopt M20 concrete and Fe500 steel. Sketch the reinforcement details