1 (a)
What is meant by normal distribution in statistics and what is the relationship between mean value and characteristics value in such distribution assuming 5% confidence limit?

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1 (b)
Derive an expression for limiting values of x

_{o}/d ratio from basic for different grades of steel used in RCC beam design. What is their importance?
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1 (c)
For a given data of a beam subjected to bending shown that \[ \dfrac {x_u}{d}=1.2 - \sqrt{ (1.2)^2 - \left ( \dfrac {6.68M_u}{f_{ck} \ bd^2} \right )}\cdot Data: \ b, d \ M_u, \ f_{ck}\ and \ f_y .\]

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1 (d)
Explain the terms balanced, over-reinforced and under reinforced section in beam subjected to flexure with neat sketches. Which of these should be recommended in deign? And Why?

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2 (a)
Determine the flexural steel reinforcement at mid span for a simply supported beam of effective span of 5.25m. The characteristic dead and live loads shall be 15kN/m and 20 kN/m respectively. The cross sectional dimensions are width is 300mm and effective depth is 675mm. Adopt M

_{20}grade concrete and Fe415 grade steel.
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2 (b)
A RC beam of section 250mm × 500mm overall dimensions is reinforced with 5 bars of 25 mm diameter on tension side and 5 bars of 12mm diameter on compression side with an effective cores of 50mm for both. Determine the ultimate moment of resistance of the section. Adopt M

_{25}grade concrete and Fe415 grade steel.d^{1}/d | 0.15 | 0.10 |

Fe415, fsc | 342 N/mm^{2} | 353 N/mm^{2} |

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3 (a)
Determine the ultimate shear strength of the support section of a RC beam with following data: width, b=300mm, effective depth, d=600mm, A

_{st}=4 bars of 25mm&straighphi;, 8mm ϕ 2 legged vertical stirrups at 150mm c/c, 2 bars of 25mm ϕ are bent up at 45° near the support. Adopt M_{25}grade concrete and Fe415 grade steel.
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3 (b)
Determine the ultimate moment of resistance of flanged beam as shown in Fig. Q3(b). Adopt M

_{20}grade concrete and Fe415 grade steel.

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4
A simply supported RC beam supports a service live load of 8kN/m over a clear span of 3m. Support width is 200mm. Adopt M

_{20}grade concrete and Fe415 grade steel. Design the beam for flexure and shea. Check the beam depth for control of deflection using empirical method. Sketch the reinforcement details.
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5
Design a two way slab of 5×7m (clear dimensions) with all four edges discontinuous and corners held down. The slab has a support width of 300mm on all the four edges. The live reinforcement details.

20 M

6 (a)
Design a circular pin ended column of 400mm diameter with helical reinforcement, with unsupported length of 4m. The column is to carry a factored axial load of 1500 kN. Adopt M

_{20}grade concrete and Fe415 steel. Sketch the reinforcement details.
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6 (b)
ARC column of size 300mm × 400 has an unsupported length of 3m and effective length 3.6m. Determine the longitudinal steel and transverse steel -if the column is subjected to a factored load of P

_{u}=1000 kN and M_{u}=210 kN-m. Adopt M_{25 }grade concrete and Fe415 grade steel. Assume d'=60mm. Sketch the reinforcement details.
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7
Design an isolated rectangular footing of uniform depth for the column size of 230mm× 300mm supporting an axial service load of 850kN-m. The safe bearing capacity of soil is 150kN/m

^{2}. Adopt M_{20}grade concrete and Fe415 grade steel. Sketch the reinforcement details.
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8
Design a dog legged staircase for a building in which the vertical distance between floors is 3.5m. The stair hall measures 2.1m×5.0m. Take live load 2 kN/m

^{2}. The fights are supported on 230mm walls at the ends of outer edges of landing slab, so that it spans in the direction of going. Adop M_{20}grade concrete and Fe415 grade steel. Sketch the reinforcement details.
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