Module 8 · Lesson 8.2
A complete beam design
One beam, from the loading to the bar schedule, with every check and nothing skipped.
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)
Worked example
A simply supported floor beam, complete
Given
- Simply supported span 7.5 m, carrying a floor
- Beam 300 mm wide × 600 mm deep (first guess, span/depth ≈ 12.5)
- Permanent load from the slab, screed and finishes: 22.0 kN/m
- Imposed load: 15.0 kN/m
- C30/37 concrete, grade 500 reinforcement, 35 mm cover, H8 links
Find
The complete reinforcement: main bars, links, and the serviceability verdict.
Assumptions
- One layer of tension bars
- Partial factors 1.35 and 1.5 — nationally determined, requiring verification
- cot θ limited to 2.5
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 Klim.
- 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. Steel is the variable you reach for when depth is fixed, and it buys strength but not stiffness.
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, fywd = 434.8 N/mm² and cot θ = 2.5. What link area per unit length Asw/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 Klim 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
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint