Structural Design for Beam (Eurocode 2)

Before we conduct structural design of a reinforced concrete beam using Eurocode 2, we need to calculate the bending moment and shear force developed in it under ultimate limit state.

The longitudinal reinforcement in beam is provided to resist the bending moment. When the beam is subjected to sagging moment, the tension face is located at the soffit and thus, reinforcement should be provided there. The opposite case should be applied for beam subjected to hogging moment. During calculation, we check whether the value of K is below Kbal. If that is the case, a singly reinforced section is sufficient. Conversely, compressive reinforcement would be required. Based on the stress diagram, we can calculate the forces developed in tensile and compressive reinforcement under equilibrium. We then determine the area of reinforcement required, and provide them accordingly while adhering to code-specified limits.

As for the design of shear stirrup, we need to determine the diagonal concrete strut inclination angle. When the angle exceeds 45 degree, we should use larger section to lower it. The ratio of two leg shear reinforcement area to stirrup spacing is first determined, and subsequently the stirrup spacing, if we know what is the steel reinforcement we want to use.

The serviceability of beam, notably deflection can be checked using method stated in the code, rather than explicitly calculate the beam deflection and compare it with limits. This avoids tedious procedure. Span-effective depth ratio is the way for this, and to use this method we need several inputs: beam support condition, length, steel grade, ratio of provided to required steel reinforcement etc.

In this worked example, we need to conduct structural design for a simply supported reinforced concrete beam subjected to permanent and variable actions of 16kN/m and 12kN/m respectively.

First, we need to apply factor of safety to the loading, and determine the design force under ULS. Then, by using the factored uniform load, we can calculate the design bending moment and shear force, which are found to be 242.55kNm and 138.6kN respectively.

For the design of longitudinal reinforcement, we need to determine the effective depth to rebar at tension face. Then, we can calculate both K and Kbal. In our case, since K is less than Kbal, a singly reinforced section would be enough to resist the design bending moment. The required area of reinforcement is found to be 1140mm2. By providing 3H25, we fulfil the requirement with As,prov equals to 1472.6mm2. This provision is deemed adequate as it lies within the minimum and maximum reinforcement area limits.

For the shear stirrup design, we first calculate the crushing strength when the strut inclination angle is at 22 degree. The value is found to be 448kN and it is greater than our design shear force. This means, we can simply adopt strut inclination angle of 22 degree when determining the stirrup requirement. As a result, the required stirrup area to spacing ratio is 0.262mm2/mm. The proposed H10-250 configuration fulfils the requirement as well as minimum limit.

Our concrete section is considered highly stressed. In relation to this, the basic span-effective depth ratio is found to be 15.18. By applying adjustment based on reinforcement area provided, the allowable span-effective depth ratio becomes 19.61. Since the actual span-effective depth ratio for the beam is 12.79, the deflection check is passed.