Reinforced Concrete Design / Reinforced-concrete beams

A complete beam design

A worked beam calculation showing how loading, bar selection, shear and serviceability interact.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

Recalculated the beam with a 650 mm depth, provided-bar neutral axis, shear links, span/depth and crack checks.

Checks needed for project use

A concrete-design reviewer must check the stated first-generation clauses, National Annex choices, detailing rules and factor sets. Numerical agreement alone does not establish code compliance.
Actual support geometry, anchorage availability, top reinforcement, exposure and fire requirements need project-specific checking.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

Every technique so far has been shown on its own. In practice they interact: the bar size chosen for bending changes the effective depth used for shear, the shear design changes where the bending bars may stop, and the bar area chosen for strength changes whether the deflection check passes. This lesson runs one beam through all of it, in order, so the interactions are visible.

By the end of this lesson you should be able to

Carry out a complete beam design without omitting a check
See how each step's output becomes the next step's input
Identify which check governed and why
Judge whether the resulting beam is sensible

What you should already know

The design sequence (previous lesson)
Flexure, shear, bond and serviceability (Modules 4, 5, 6)

Revised 300 × 650 mm teaching section. Support anchorage and the top cage detail must be completed for the chosen support arrangement.

Worked example

A simply supported floor beam: checked reinforcement

Given

Simply supported span 7.5 m; rectangular beam 300 mm wide × 650 mm deep
External permanent load 22.0 kN/m, excluding all beam self-weight; imposed load 15.0 kN/m
C30/37, grade 500 reinforcement, nominal cover to links 35 mm, H8 links
One layer of 3H32 bottom bars; maximum aggregate size assumed 20 mm

Find

Select and check the main bars and links, then calculate serviceability and the required end anchorage. Support-detail acceptance remains open until the support geometry is provided.

Assumptions

First-generation teaching values: γG = 1.35, γQ = 1.5, αcc = 0.85, γc = 1.5, γs = 1.15; no redistribution; adopted x/d limit 0.45
Uniform loading, simple supports and good bond; cot θ = 2.5; use full support shear without a near-support reduction
For the illustrative long-term crack check: ψ2 = 0.3, creep coefficient 2.0, kt = 0.4 and crack-width limit 0.30 mm
Brittle partitions are assumed, so apply 7.0/7.5 to the span/depth limit

What to change, and what changing it costs

Suppose this beam has to be shallower — 500 mm instead of 600, because of a services zone. What happens?

d falls from 541 to 441, so K rises from 0.156 to 0.234, well above K_lim.
The beam now needs compression reinforcement, which is more bars, more congestion at the support, and a doubly reinforced calculation.
ρ rises, so the basic span/depth ratio falls, while l/d rises from 13.9 to 17.0. The deflection check now almost certainly fails.

So the 100 mm of depth was not a small change. Depth is the single most powerful variable in a concrete beam, because it appears squared in the bending capacity and directly in the stiffness. When depth is fixed, reinforcement can increase both resistance and cracked-section stiffness, subject to ductility, congestion and serviceability checks.

Practice

A 300 × 600 beam (d = 541 mm) in C30/37 carries a design moment of 409.7 kNm. What is K?

Practice

The same beam carries a design shear of 218.5 kN with z = 486.9 mm, f_ywd = 434.8 N/mm² and cot θ = 2.5. What link area per unit length A_sw/s is required, in mm²/mm?

Practice

For that beam, what is the maximum link spacing permitted by the detailing rule, in mm?

Practice

If the beam depth were reduced to 500 mm (d = 441 mm) with the same moment, what would K become?

Summary

The design is a sequence, and each step's output is the next step's input
K against K_lim decides the section type before any steel is computed
Bars must fit: 5 H25 has enough area for this beam and cannot be built in it
Link spacing has two independent limits — strength and the detailing rule
Rounding up at bar selection does real work in the deflection check
Depth is the most powerful variable: it is squared in strength and direct in stiffness