Assignment - 1 AR 303B Last Date of submission: 01/10/2011. Submit the assignment on only A4 size sheet. 1. Define terms Neutral Axis, Critical Neutral Axis, Balanced Neutral Axis and draw diagrams to show these sections. 2. Derive expressions for calculating critical N. A. and Balanced N. A. for a section when the stresses developed in the section and the area of steel provided is known. 3. 4. 5. Draw diagram of a singly reinforced section to i) Overall depth ii) Effective depth iii) Effective iv) Clear cover v) Tensile Steel vi) Anchor vii) Shear Stirrups show: Cover Bars Draw stress diagram for a singly reinforced beam section and show on it: i) Tension Zone iv) Lever Arm ii) Compression Zone iii) Neutral Axis Derive the expressions for calculating the neutral axis depth factor (k) , lever arm depth factor (j), moment of resistance coefficient (R) and the percentage of steel (p) if the given section is a singly reinforced balanced section. 6. A simply supported singly reinforced rectangular beam is 200mm wide has an effective depth as 600mm. It has 4 bars of 16mm Ø as tension reinforcement. Determine whether the given section is a balanced section or an over reinforced section or an under reinforced section. Also calculate the UDL, excluding the self weight, the simply supported beam can carry over an effective span of 6m if M20 concrete, Fe415 steel is used having modular ratio 13.33. 7. An R. C.C. beam 300mm x 550mm overall is reinforced with 3 bar of 20mm Ø. The effective cover is 50 mm. Find the moment of resistance and the safe load (inclusive of self load) which the beam can carry over an effective span of 5m. Take σ cbc = 7 N/mm2 and σst = 230 N/mm2 and m = 13.33. 8. A singly reinforced concrete beam 300mm wide has an effective depth of 500mm. The effective span of the beam is 5m. It if reinforced with 804mm 2 of steel. If the beam carries a total load of 16KN/m on the whole span, determine the stresses produced in concrete and steel if M20 concrete and Fe415 steel are used. 9. A singly reinforced beam 350mm wide and 550mm deep has an effective span of 6m and carries an all inclusive load of 20 KN/m2. The beam is reinforced with 4 bars of 20mm Ø at en effective cover of 35mm. Find the maximum stresses produced in concrete and steel. Take m = 13.33 10. A singly reinforced rectangular beam 350mm wide has a span of 6.25m and carries an all inclusive load of 16.30 KN/m. If the stresses in concrete and steel shall not exceed 7 N/mm2 and 230 N/mm2 find the effective depth and the area of tension reinforcement. 11. A singly reinforced beam has a span of 5m and carries a uniformly distributed load of 25 KN/m. The width of the beam is chosen to be 300mm. Find the depth and the area of steel required for a balanced section. Use M20 concrete and Fe415 steel. 12. Design a singly reinforced beam section subjected to a maximum bending moment of 55.35 KNm. The width of the beam may be made two third of the effective depth. Use M20 concrete and Fe415 steel. 13. An R.C. beam of span 5m is 250mm wide and 500mm deep to the centre of tensile reinforcement, which consists of 4 bars of 22mm Ø. The beam carries a load of 30 KN/m inclusive load of its weight. Design the shear reinforcement consisting of stirrups. Use M20 concrete and Fe415 steel. 14. An R. C. C. beam of span 6.50m is 300mm wide and 750mm deep to the centre of the tensile reinforcement which consists of 6 bars of 20mm Ø. The beam carries a load of 290KN at its centre. Design the shear reinforcement if 50% of the tensile reinforcement is curtailed near the support. Also check the beam in bond. Use M20 concrete and Fe415 steel. 15. A reinforced rectangular beam of span 5m is 300mm wide and 550mm deep to the centre of the tensile reinforcement which consists of 4 bars of 22mm Ø. The beam carries a load of 20 KN/m inclusive of its weight. Design the shear reinforcement for the beam. Use M20 concrete and Fe415 steel. 16. A R. C. C. beam 300mm x 750mm is simply supported over a clear span of 5.5m. It carries an udl of 50 KN/m length. The section is reinforced with 6-25 Ø bars at an effective cover of 50mm. Using M20 grade of concrete and HYSD bars, design the shear reinforcement for the following cases and also check the beam for end anchorages: a) When only vertical stirrups are used. b) When two bars are bent up on the same cross section at 45o.