## Limit state Method for Reinforced concrete stuctures - May 16

### Civil Engineering (Semester 7)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question No. 1 is compulsory

(2) Attempt any three out of remaining five questions

(3) Draw neat diagrams wherever necessary

Attempt any FOUR

**1(a)** What is limit state? What are the various limit states in RCC?
(5 marks)

**1(b)** State the assumptions made in the Limit State of Collapse (flexure) in RCC. Also draw strain and stress diagram across the section.
(5 marks)

**1(c)** Draw the sketch of a way and two way.
(5 marks)

**1(d)** Write any four assumptions in Ultimate Load Design method in RCC. Also sketch the stress block used in this method.
(5 marks)

**1(e)** What is strap footing? When it is provided? Also draw of strap footing.
(5 marks)

**1(f)** Derive stress block parameters in limit state method for collapse (flexture).
(5 marks)

**2(a)** Determine the area of tension steel reinforcement for the beam having dimensions 300mm X 55mm (effective), it is subjected to a hogging bending moment of 120kNm. Also draw stress diagram across the section.

Use (i) $M_{25}$ concrete and $Fe_{415}$ steel (ii) $M_{20}$ concrete and $Fe_{250}$ steel. (10 marks)

**2(b)** A beam of size 300 X 550 mm overall, is subjected to a factored bending moment of 295 kNm. Compute the reinforcement required at an effective cover of 50mm to compression and tension reinforcement.

Use $M_{25}$ concrete and $Fe_{415}$ steel.

d'/d | 0.05 | 0.100 | 0.15 | 0.20 |
---|---|---|---|---|

$f_{sc} (MP_a) $ | 355 | 353 | 342 | 329 |

(10 marks)

**3(a)** A reinforced concrete beam of 300 X 550 mm overall is reinforce with 5 bars of 20mm $\varphi$ HYSD steel of grade $Fe \space 500$, placed at an effective cover of 50mm. The beam carries a factored UDL of 120 kN/m (working) over a simply supported clear span of 5m. Design the shear reinforcement. Use M20 concrete. Also sketch the shear reinforcement details.

pt % | 0.50 | 0.75 | 1.0 | 1.25 | 1.5 | 1.75 |
---|---|---|---|---|---|---|

$\tau_c \space MP_a$ | 0.48 | 0.56 | 0.62 | 0.67 | 0.72 | 0.75 |

(10 marks)

**3(b)** A ice beam having 1250mm effective width of flange has thickness of flange equal to 110 mm. The effective depth of the beam is 600mm and width of the web is 300mm. It is reinforced with 6 bars of 20mm $\varphi$ on the tension side. Determine moment of resistance if M25 concrete and $Fe_{415}$ steel is used. Use LSM.
(10 marks)

**4(a)** Design a circular column of diameter 400mm, subjected to aload of 1350kN. The column is having spiralties. The column as 2.9m effective length. Use M25 concrete and $Fe_{415}$ steel. Use LSM.
(8 marks)

**4(b)** A hall of a residential building measured $4.1m X 5.8m$. It is supported by 300mm thick wall on all four sides. Design the simply supported slab using M20 and HYSD $Fe_{415}$ steel. Assume the live load on the slab as $3kN/m^2$ and floor finish load as $1kN/m^2$. Apply checks for shear, deflection and development length.

Sketch the reinforcement details along both spans

$Ly/Lx$ | 1.3 | 1.4 | 1.5 | 1.75 |
---|---|---|---|---|

$a_x$ | 0.093 | 0.099 | 0.104 | 0.113 |

$a_y$ | 0.055 | 0.051 | 0.046 | 0.037 |

(12 marks)

**5(a)** Write step by step procedure to design one way slab with all required checks.
(4 marks)

**5(b)** A rectangular beam of size $300 X 450 mm$ overall is reinforced with 4 bars of 20mm $\varphi$ as tension reinforcement. It is subjected to a shear force of 20kN and a bending moment of 20kNm. In addition to this, it also carries torsional moment of 2kNm. Design the beam for combined BM, SF and TM. Another 50mm as effective cover to the tension & compression reinforcement. Use M20 and $Fe_{415}$ as grades of the materials.
(8 marks)

**5(c)** A RCC beam of size 260 X 550mm effective depth is reinforced with 3 bars of 16mm dia. in tension zone. Determine moment of resistance using Ultimate load method in RCC. Use M25 and $Fe_{415}$ as the materials. Also draw stress block across the section.
(8 marks)

**Q6)** Design the combined footing for two column Cl of size 400 X 400 mm and C2 of size 500 X 500 mm in size and carrying 500KN and 800KN as working loads respectively. The columns are spaced at 4m apart. The available width restriction is 2.4m. The smaller column is 0.4m away from the property line. The SBC of the soil is $140kN/m^2$. Use M25 and $Fe_{415}$. Sketch reinforced in details.
(20 marks)