YS-RCS-BS-03

BEAM DESIGN

Problem

Design a grade 45, 200mm x 600mm reinforced concrete beam subjected to the following design forces:

• Left support - hogging moment 100kNm, shear 30.7kN, torsion 10kNm.
• Span - sagging moment 50kNm, shear 0kN, torsion 5kNm.
• Right support - hogging moment 100kNm, shear 50kN, torsion 0kNm.

This 5m beam is an end span of a continuous beam. Take the cover to reinforcement as 25mm.

Solution

1. Arrange the reinforcement in beam section.
2. Determine the effective depth to tension reinforcement.
3. Determine whether singly reinforced section is sufficient as per cl.3.4.4.4, BS8110-1:1997.
4. Determine the lever arm of tension reinforcement in beam section using the formulation provided in cl.3.4.4.4, BS8110-1:1997.
5. Determine the depth to neutral axis in beam section using the formulation provided in cl.3.4.4.4, BS8110-1:1997.
6. Determine the effective depth to compression reinforcement if doubly reinforced section is required, in accordance with cl.3.4.4.4, BS8110-1:1997.
7. Calculate the ratio of effective depth to compression reinforcement : depth to neutral axis as per cl.3.4.4.4, BS8110-1:1997, and then determine the yield strength of compression reinforcement.
8. Determine the area of compression reinforcement required based on cl.3.4.4.4, BS8110-1:1997.
9. Determine the area of tension reinforcement required based on cl.3.4.4.4, BS8110-1:1997.
10. Check whether the area of compression and tension reinforcements provided are greater than minimum requirement as stated in Table 3.25, BS8110-1:1997, while less than maximum limit as per cl.3.12.6.1, BS8110-1:1997.
11. Calculate design shear stress developed in beam section as per cl.3.4.5.2, BS8110-1:1997.
12. Determine concrete shear strength based on the method provided in Table 3.8, BS8110-1:1997.
13. Calculate the Asv/Sv required based on Table 3.7, BS8110-1:1997.
14. Provide sufficient Asv/Sv by manipulating the shear link diameter and spacing.
15. Determine the diameter and numbers of side bar to resist torsion.
16. Calculate the spacing of the bars and check whether they exceed the limits as stated in cl.2.4.9, BS8110-2:1985.
17. Calculate torsional shear stress developed in beam section by referring to cl.2.4.4.1, BS8110-2:1985.
18. Determine the total shear stress in beam section as per cl.2.4.5 & cl.2.4.6, BS8110-2:1985.
19. Calculate the Asv/Sv required to resist torsional shear stress in accordance with cl.2.4.7, BS8110-2:1985.
20. Calculate the total Asv/Sv required to resist shear and torsion. Then, check whether the provision of link fulfills the requirement (cl.2.4.8, BS8110-2:1985).
21. Check whether the surplus area of reinforcement in tension and compression zones is sufficient to fulfill the requirement to resist torsion, as per cl.2.4.9, BS8110-2:1985.
22. Based on the support condition of beam, determine the basic span to effective depth ratio by referring to Table 3.9, BS8110-1:1997.
23. Calculate the stress developed in reinforcing steel by referring to Table 3.10, BS8110-1:1997.
24. Determine the modification factor due to tension reinforcement based on Table 3.10, BS8110-1:1997.
25. Determine the modification factor due to compression reinforcement based on Table 3.11, BS8110-1:1997.
26. Calculate length factor based on beam length, referring to cl.3.4.6.4, BS8110-1:1997.
27. Calculate the permissible span to effective depth ratio by multiplying the basic ratio with modification factor and length factor.
28. Check whether the actual span to effective depth ratio exceeds the permissible ratio.
29. Determine the maximum allowable rebar spacing based on the formulation provided in cl.3.12.11.2.4, BS8110-1:1997.
30. Determine the minimum rebar spacing by referring to cl.3.12.11.1, BS8110-1:1997.
31. Check whether the actual rebar spacing lies between the minimum and maximum limits, as calculated in steps above.