---
title: "Dog-legged stair, 5.0 m by 4.0 m"
subject: "Building Technology"
chapter: 5
key: "semester_6/building_technology:dog-legged-stair-public-5m"
source: https://www.bctengineer.com/q/semester_6/building_technology/dog-legged-stair-public-5m
site: BCT Engineering
---

# Dog-legged stair, 5.0 m by 4.0 m

Building Technology · Chapter 5: Stair, lifts and escalators

- Asked in: 2065 Shrawan (old course), 16 marks
- Video: [Design of RCC Dog-Legged Stair | Staircase | Design of Stair | Building design | Structural Design](https://www.youtube.com/watch?v=ZSurkcbC7GA) — Visual Civil
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/building_technology/dog-legged-stair-public-5m
- Whole chapter: https://www.bctengineer.com/md/semester_6/building_technology/chapter-5

## Question

Define stair. What are the functional requirements of good stair? Design a dog-legged staircase for a public building in a room of 5.0m×4.0m and floor to floor height 3.0m. Assume necessary data. Give neat and clean sketch to support your design.

## Short answer

Stair: a series of steps connecting floors. Key requirements: comfortable rise and tread (2R+T≈600 mm), max 12 steps per flight, adequate width, landings, headroom. For 3 m height in 5×4 m: 20 risers of 150 mm, treads 300 mm; two flights of 10 risers each, flight width 1.9 m, waist slab 250 mm.

## Answer

A **stair** is a set of steps (a series of risers and treads) that connects floors at different levels, giving access from one storey to another, usually with landings and a balustrade.

#### Functional requirements of a good stair
1. **Location:** easily accessible, centrally placed, well lit and ventilated, and near the main entrance; not reached through rooms.
2. **Width:** residential at least 0.9-1.0 m, public buildings 1.5 m or more (as per NBC and local building bye-laws), so that two persons can pass.
3. **Easy and safe ascent:** riser 150-175 mm (public buildings not more than 150 mm), tread 250-300 mm; $2R + T$ about 580-600 mm; all steps in one flight equal.
4. **Pitch:** between 25 and 40 degrees.
5. **Number of steps per flight:** not more than 12 and not less than 3.
6. **Landings:** provided at turns and between flights, with width not less than the stair width.
7. **Headroom:** at least 2.0-2.2 m clear above every step.
8. **Strength and fire resistance:** strong enough for the live load; fire-resistant material, with a separate fire-escape stair in tall buildings.
9. **Handrails and balustrades:** about 0.9 m high, strong and safe for children.
10. **Surface:** non-slip treads, good lighting and ventilation, durable and pleasing in appearance.

#### Given data and assumptions
- Stairwell (internal): 5 m x 4 m; floor-to-floor height $H = 3$ m; stair for a public building, RCC.
- Assumed riser $R = 150$ mm and tread $T = 300$ mm; flight width $b = 1.9$ m. Wide flights of 1.9 m (public building) leave a gap of 4.0 - 2 x 1.9 = 0.2 m between the flights.

#### Design
1. **Number of risers** $= H/R = 3/0.15 = 20$, adopt **20 risers**; exact riser $= 3/20 = 150$ mm.
2. **Flights:** a dog-legged stair has two equal flights, so each flight has 20/2 = 10 risers and 10-1 = 9 treads (the landing or upper floor acts as the last tread).
3. **Going of one flight** $= 9 \times 0.3 = 2.7$ m.
4. **Width:** two flights of 1.9 m side by side need $2b = 3.8$ m; the remaining $W - 2b = 4 - 3.8 = 0.2$ m is the gap between the flights.
5. **Landing:** a half-space landing 1.9 m x 4 m (full stairwell width) at height $= 10 \times 0.15 = 1.5$ m.
6. **Length check:** going + landing $= 2.7 + 1.9 = 4.6$ m $\le 5$ m, so it fits; the spare 0.4 m is kept as entry/exit space.
7. **Check:** $2R + T = 2 \times 150 + 300 = 600$ mm (within 550-650 mm); pitch $= \tan^{-1}(R/T) = 26.6^\circ$ (within 25-40 degrees).
8. **Waist slab:** effective span about 4.6 m, so depth $\approx$ span/20 $= 230$ mm; adopt a 250 mm thick waist slab (reinforcement to be designed separately). Provide a handrail 0.9 m high, 20-25 mm nosing and a non-slip finish.

#### Plan and section
```text
 +------------------------+---------+
 | FLIGHT 2  <<<<<<  UP   |         |
 | 9 treads               | LANDING |
 +------------------------+ (b x W) |
 | FLIGHT 1  >>>>>>  UP   |         |
 | 9 treads               |         |
 +------------------------+---------+
 <-------- going -------> <-- b -->
 (entry at left end of flight 1; arrows point up the stair)
```
```text
 SECTION (not to scale)
                          +---- upper floor 3 m
                    _____|
               ____|   flight 2
        ______|  landing
   ____|  flight 1
 _|
 ground floor +0.00
```

#### Summary
| Item | Adopted |
|---|---|
| Riser | 150 mm (20 nos.) |
| Tread | 300 mm |
| Flights | 2 flights x 10 risers |
| Width of flight | 1.9 m |
| Waist slab | 250 mm |

**Answer: 20 risers of 150 mm and treads of 300 mm; 2 flights x 10 risers; flight width 1.9 m.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is a stair?
   A. A sloping ramp without steps between floors
   B. A set of steps (risers and treads) connecting floors at different levels
   C. A single horizontal platform between two walls
   D. A railing fixed along a floor opening
   Answer: B. A stair is a series of risers and treads that gives access from one storey to another, usually with landings and a balustrade. (Key point: Definition of stair)

2. Which set of values matches the functional requirements of a good stair?
   A. Pitch 45-60 degrees, 20 steps per flight, no landings
   B. Public width 0.6 m, riser 250 mm, tread 100 mm
   C. Pitch 25-40 degrees, 3 to 12 steps per flight, landing not narrower than the stair width
   D. Pitch under 10 degrees, steps unequal, headroom 1.0 m
   Answer: C. Good stairs have pitch 25-40 degrees, 3-12 steps in a flight, equal steps and landings at least as wide as the stair. (Key point: Functional requirements)

3. For H = 3 m and R = 150 mm, how is the dog-legged stair arranged?
   A. 20 risers; 2 flights of 10 risers with 9 treads each
   B. 20 risers; 2 flights of 20 risers each
   C. 30 risers; 2 flights of 15 risers
   D. 20 risers; 2 flights of 10 risers with 10 treads each
   Answer: A. 3/0.15 = 20 risers, two equal flights of 10 risers, and 10 - 1 = 9 treads because the floor is the last tread. (Key point: Risers and flights)

4. With b = 1.9 m, going 2.7 m and a 5.0 m x 4.0 m stairwell, which statement is correct?
   A. Well gap is 1.9 m and the stair does not fit
   B. Well gap is 0.2 m and going + landing = 4.6 m fits within 5 m
   C. Well gap is 0.2 m and going + landing = 5.4 m exceeds 5 m
   D. Well gap is 0.5 m and going + landing = 4.6 m
   Answer: B. Gap = 4 - 3.8 = 0.2 m; going 2.7 + landing 1.9 = 4.6 m <= 5 m, leaving 0.4 m spare. (Key point: Width and length check)

## Related in Building Technology

- [Dog-legged RCC stair design for 3 m floor height](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Astair-dog-3m-assume) — Building Technology, chapter 5, asked 3×
- [Dog-legged stair, 4.5 m by 3.0 m lobby](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Adog-legged-stair-lobby-4p5m) — Building Technology, chapter 5
- [RCC dog-legged stair for office building](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Arcc-stair-office-building) — Building Technology, chapter 5
- [Dog-legged stair design with elevators and ramp](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Astair-078c) — Building Technology, chapter 5
- [Dog-legged RCC stair, 4.6 m by 2.6 m](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Adog-legged-stair-residential-4p6m) — Building Technology, chapter 5, asked 3×
- [Vertical circulation elements; RCC dog-legged stair](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Astair-circulation-068ba) — Building Technology, chapter 5