Design of Beam- RCC Singly Reinforced

Table of Content for Design of Beam-RCC Singly Reinforced

• Types of Beams
• Types of Loads
• Determination of beam size
• Determination of Loads and Moments
• Calculation of Main reinforcement
• Shear or Transverse Moments
• Check for Bond
• Curtailment and Splicing details

A beam is a horizontal structural member subjected to the loads on the transverse direction. The beam can be straight, curved or circular in plan. The most common beam section used in civil works is rectangular. However, the beam can be circular, T-shaped, L-shaped, or square in section.

The beam can also be classified on the basis of support conditions. Such as-

1. Simply Supported Beam- The beam supported on both of its ends. The ends can be pin jointed or roller supported. The ends are allowed to rotate but not allowed to move in the direction of the load.
2. Cantilever Beam- The cantilever beam has one end fixed and the other end free. The fixed end is not allowed to displace or rotate. The free end of the beam can rotate as well as displaced.
3. Fixed Beam- The beam having both ends fixed is called a fixed beam. Both of the ends of the beam are not allowed to rotate or displace.
4. Continuous Beam- The beam supported on more than two support is called a continuous beam.

Types of Loads-

Before starting the design of the beam, it is necessary to understand the types of loads acting on the structure and their critical combination.

1. Dead Load (DL)- It is the self-weight of the structure, fixed equipment, flooring, ceiling or anything that will not move during the lifetime of the structure. IS 875 (Part 1) specifies unit load for the material for dead load estimation.
2. Live Load (LL)- It is the load due to people, furniture or anything that moves or may be moved from one place to another. IS 875 (Part 2) specifies the live load for various types of structures.
3. Rain load (RL)- The load due to rain. It is considered for the roof only.
4. Snow Load SL)- The load due to snow. It is considered for the roof only. IS 875 (Part 4).
5. Wind Load (WL)- The load on the structure due to wind is called wind load. It acts transverse to the structures. IS 875 (Part 3).

Earthquake Load (EL)- It is due to the earthquake. It also acts in the horizontal direction of the structure similar to wind load. IS 1893:1984

Since all of these loads do not act at the same time and hence their critical combination is used for the design of the beam. IS 875 (Part 5) gives a specification for load combination. Some of these combinations are as follows-

1. 1.2 DL + 1.6 LL
2. 1.2 DL + 1.0 EL + 0.2 SL
3. 1.2 DL + 1.6 (SL or RL)
4. 0.9 DL + 1.0 (WL or EL)
5. 1.2 DL + 1.0 WL + 0.5 (SL or RL)

Note-

*The Rain load and Snow load are not considered together only higher of the two is taken. Since both of them are used for roof design thus no Live load is considered.

*Only the higher value out of Earthquake load and wind load is considered for the critical combination of the load.

Design of Beam-

The aim of the design is the achievement of an acceptable probability that structures being designed satisfactorily during their intended life. With an appropriate degree of safety, they should sustain all the loads and deformations of normal construction and use and have adequate durability and adequate resistance to the effects of misuse and fire.

Steps for Design of Beam-

In this section, we will highlight the details to design the beam as per IS 456:2000. The steps for the same are as follows-

1. Determine the size of the section
2. Estimate the loads and moments
3. Calculate the main reinforcement
4. Check for shear and calculation of shear reinforcement
5. Check for Bond
6. Curtailment and splicing details

Determination of Beam Size-

The first step in the design of beam is to determine the size of the beam.

The depth of the beam is governed by the span to depth ratio. IS 456:200 specifies the span-depth ratio as follows-

As per IS 13920:1993, the depth of the beam should not be more than 1/4^th of the clear span and the width to depth ratio should be more than 0.3. However, the width of the beam should not be lesser than 200mm.

It should also be kept in mind while designing the beam that its’ width should not be greater than the width of the columns on which it is supported.

Thumb Rule- For every 0.3m of clear span, the depth of the beam should be 25mm.

Estimation of Loads and Moments-

The self-weight of the dead weight of the member can be calculated after defining member size.

Weight of Member= Volume of the member x Density of Concrete

The density of concrete can be taken as 2500 kg/cum.

The estimation of live load is done as per IS 875 (Part-II).

The maximum bending moment and shear force occurring due to the combination of loads are determined and the beam is designed for the same.

Calculation of Main Reinforcement (Ast)-

The IS 456:2000 recommends the use of Limit State of Method. However, Working Stress Method can be adopted where LSM is inconvenient. Thus, for the design of the beam in this article, we will adopt the limit state method only.

The main reinforcement for balanced section is calculated as-

Where, x_u (neutral axis) is 0.53d, 0.48d and 0.43d for Fe250, Fe415 and Fe500 respectively. And b is the width of the beam, d is effective depth of the beam, M_u is the ultimate moment, and f_y is yield stress of steel.

The area of tension steel required should be checked against the minimum & maximum requirement as follows-

Minimum Reinforcement-

Maximum Reinforcement– 4% of cross section of beam.

Side Face Reinforcement- Where the depth of the web in a beam exceeds 750mm, side face reinforcement shall be provided along with the two faces. The total area of such reinforcement shall be not less than 0.1 percent of the web area and shall be distributed equally on two faces at a spacing not exceeding 300 mm or web thickness whichever is less.

Selection of diameter of bar for Main reinforcement-

The diameter of main reinforcement to satisfy the minimum spacing specified between the bars which are equal to the greater value of the following- diameter of bar or 5mm+nominal max size of aggregate.

The max spacing between the bars should be 300 mm, 180 mm and 150 mm for Fe250, Fe415, Fe500 respectively.

Minimum Diameter of bar for Main Reinforcement- 12 mm.

Shear or Transverse Reinforcement (A_sv)-

V_u is Factored shear force.

Determine Design Shear Strength of Concrete (ꚍ_c) from the following table-

This value increases with an increase in the percentage of steel and grade of concrete. It has a maximum limit (ꚍ_{c max}) as given below-

If ꚍ_v < ꚍ_c, provide minimum shear reinforcement as follows-

If ꚍ_c <ꚍ_v < ꚍ_{c max} , provide shear reinforcement for-

Where, V_us= V_u – ꚍ_c.bd and S is spacing of stirrups.

If ꚍ_c < ꚍ_{c max}<ꚍ_v , the section is to be redesigned.

Spacing of Stirrups- It should be greater of 0.75d or 300 mm whichever is smaller.

Minimum diameter of bar for Stirrup- 8 mm.

Check for Bond-

The calculated tension or compression in any bar at any section shall be developed on each side of the section by an appropriate development length or end anchorage or by a combination thereof.

Development Length-

For deformed bars design bond stress values may be increase by 60%.

For bars in compression, the design bond stress can be increased by 25%.

Development length to be increased by 10%, 20% and 33% for two, three and four bundled bars in contact respectively.

Curtailment and Splicing Details for Design of Beam-

1. There should be at least one bar at every corner of the stirrup.
2. For curtailment, reinforcement shall extend beyond the point at which it is no longer required to resist flexure for a distance equal to the effective depth of the member or 12 times the bar diameter, whichever is greater except at simple support or end of the cantilever.
3. At least one-third the positive moment reinforcement in simple members and one fourth the positive moment reinforcement in continuous members shall extend along the same face of the member into the support to a length equal to L_d/3.
4. When a flexural member is part of the primary lateral load resisting system, the positive reinforcement required to be extended into the support as described in (a) shall be anchored to develop its design stress in tension at the face of the support.
5. Where splices are provided in the reinforcing bars they shall as far as possible be away from the sections of maximum stress and be staggered. It is recommended that splices in flexural member should not be at sections where the bending moment is more than 50% of the moment of resistance; and not more than half the bars shall be spliced at a section.
6. The spacing of shear reinforcement can be increased suitably at the middle L/6 span of the beam.

For more on Limit State Method, read here.

For more on Reinforcement, read here.

For more on cement, read here.

Happy Engineering!