## Theory of Reinforced and Prestressed Concrete - December 2014

### MU Civil Engineering (Semester 6)

Total marks: --

Total time: --
INSTRUCTIONS

(1) Assume appropriate data and state your reasons

(2) Marks are given to the right of every question

(3) Draw neat diagrams wherever necessary
**1 (a)** A short column 300mm × 300mm is reinforced with 4 bars of 20mm diameter. Determine the safe working load on the column. Use M20 grade of concrete and Fe415 grade of steel.
5 marks

**1 (b)** Derive the expression for balanced moment of resistance for a singly reinforced rectangle section.
5 marks

**1 (c)** Name different methods of post-tensioning. Discuss any one method in details.
5 marks

**1 (d)** Why is necessary of using high strength concrete and high steel in prestressed concrete.
5 marks

**2 (a)** Design a simply supported beam subjected to u.d.l of 40 kN/m. The width of the beam is bars of 16 mm diameter in compression and 4 bars of 16 mm dia. In tension. Determine Moment of resistance of the section. Use M20 grade of concrete and Fe415 grade of steel.
5 marks

**3 (a)** A Reinforced concrete Tee beam has the following dimension:

Flange width 1000 mm

Width of Rib 230 mm

Depth of Rib 400 mm

Depth Of flange 120 mm

Steel provided 4 no of 20mm diameter bars.

span 8.0 meter

Grade of concrete M20 and Steel Fe415

Find the safe UDL the beam can carry.
5 marks

**3 (b)** A rectangle beam 230mm × 450mm (effective depth) is reinforced with 6 bars of 16 mm diameter out of which two bars are bent at 45°. Determine the shear resistance of bent up bars and additional shear reinforcement required if the shear force is 200 kN. Design shear reinforcement adopt M20 and Fe415.

5 marks

**4 (a)** A column is 400mm× 600mm is reinforced with 8 bars of 16 mm diameter it is subjected to compressive force of 450 kN. Mx=50 kNm My=40 kNm check the safety of the column as uncracked section. Use M20 grade of concrete and Fe 415 grade of steel.

5 marks

**4 (b)** Design a simply supported slab having dimension 4m × 6m. Assume live load of 4kN/m^{2} and floor finish of 1 kN/m^{2}. Use M20 grade of concrete and Fe415 grade of steel.

α_{x}=0.089 α_{y}=0.056.
5 marks

**5** Design the isolated sloped footing (rectangular) for a reinforced concrete column 230mm× 450mm carrying axial load of 1200kN. The bearing capacity of soil is 150kN/m^{2} . Use M20 grade of concrete and Fe415 grade of steel. Draw sketch showing reinforcement details.
5 marks

**6 (a)** A PSC beam 230mm×450mm is used over an effective span of 5m to support an imposed load of 4 kN/m. Determine the magnitude of prestressing force located at 60mm from the soffit of the beam at mid span, where permissible stresses in tension are limited to 1 N/mm^{2} at service stage consider 15% loss of stresses in steel. Cable is parabolic and concentric at support. Determine stresses in extreme fibers at services at quarter span.
5 marks

**6 (b)** An I-section prestressed concrete beam has top flange 1000 mm ×200mm, bottom flange 600mm×200mm and web is 200m×200mm depth. Determine the efficiency of the section.
5 marks

**7** A prestress concrete beam (I-section) has top flange 1400 mm × 200mm, bottom flange 700 mm × 200 mm and web 180mm × 2000 mm (depth) is prestressed with wires having area 300mm^{2} located at 50mm from soffit and carrying initial stress of 1200 N/mm^{2} the span beam is 10 m calculate the percentage loss of stress in wires if

i) beam is pretensioned

ii) the beam is post-tensioned use the following data.

Es-200 kN/mm^{2} and Ec=35kN/mm^{2} Relaxation of steel stress=5% of the initial stress.

Shrinkage of concrete =300 × 10^{-6} for pretensioning and 200×100^{-6} for post tensioning creep co-efficient=1.6 slip at anchorage =1mm frictional co-efficient for wave effect 0.0015/m.
"
5 marks