---
title: "Legal and standard axle load; rigid stresses; joint spacing"
subject: "Transportation Engineering II"
chapter: 2
key: "semester_7/transportation_engineering_ii:legal-standard-axle-stresses-contraction-joint"
source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/legal-standard-axle-stresses-contraction-joint
site: BCT Engineering
---

# Legal and standard axle load; rigid stresses; joint spacing

Transportation Engineering II · Chapter 2: Highway Pavement

- Asked in: 2071 Chaitra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/legal-standard-axle-stresses-contraction-joint
- Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-2

## Question

What do you understand by legal axle load and standard axle load? Describe the stresses induced in the rigid pavement slab. How spacing between contraction joints is calculated in jointed plain concrete pavement?

## Short answer

Legal axle load is the maximum permitted by law (≈10.2 t single axle); standard axle is 80 kN used in design. Rigid slab stresses include load (flexural), warping (temperature gradient), and friction. Contraction joint spacing is limited by sub-base friction stress: Lc = (2×10⁴ Sc)/(W f) ≈ 4.5 m for plain concrete.

## Answer

#### Legal axle load and standard axle load
- **Legal axle load** is the maximum axle load permitted by law on public roads; it is the legal limit for a single axle (about 10.2 t for a dual-tyre single axle in India/Nepal, as per Nepal Road Standards / transport rules) and for tandem axles. Loads above it are overloads and cause rapid damage.
- **Standard axle load** is the reference axle used in design: a single axle of 80 kN (8.16 t, 18 kip) with dual wheels. All other axle loads are converted to it by the fourth power law $(P/80)^4$ to get cumulative standard axles (msa) in IRC:37 and AASHTO ESAL.

#### Stresses induced in a rigid pavement slab
1. **Load stresses** (flexural, from wheel loads) - interior, edge and corner stresses by Westergaard and Kelly. The edge stress is usually the largest bending stress, the corner load gives the largest deflection and cracks at corners.
2. **Warping stress** - from the temperature difference between top and bottom of the slab (tension at bottom by day, at top at night). Bradbury: $\sigma_{te}=\dfrac{CE\alpha\Delta T}{2}$.
3. **Frictional stress** - from restraint to the slab movement by the sub-base: $\sigma_f=\dfrac{WLf}{2\times10^4}$, tension when the slab contracts.
4. **Stress due to expansion** (compression) when joints are blocked, and shrinkage stress in early age.
5. **Subgrade-related stresses** - settlement and pumping lead to loss of support and cracking.

#### Spacing between contraction joints in jointed plain concrete pavement
Contraction joints are placed so that the tensile stress caused by sub-base friction at the middle of the slab does not exceed the allowable tensile stress of the (young) concrete.

$$
\sigma_f=\frac{W\,L\,f}{2\times10^{4}}\le S_c\ \Rightarrow\ L_c=\frac{2\times10^{4}\,S_c}{W\,f}
$$

where $W$ is the unit weight of concrete (2400 kg/m3), $f$ the coefficient of friction (1.5) and $S_c$ the allowable tensile stress in concrete (about 0.8 kg/cm2 for young concrete). So $L_c=\dfrac{2\times10^4\times0.8}{2400\times1.5}=4.4$ m, which gives the practical spacing of 4.5 m (IRC:58). For reinforced slabs, $L_c=\dfrac{2S_sA_s}{W h f}$ with $S_s$ the allowable steel stress and $A_s$ the steel area per metre width. The spacing also keeps warping stresses (through $L/l$) acceptable.

## Check yourself

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

1. What is the difference between a legal axle load and a standard axle load?
   A. Legal is the maximum permitted by law; standard is the 80 kN reference axle used to convert other loads in design
   B. Legal is 80 kN; standard is the maximum by law
   C. They are the same load called by different names
   D. Standard is the average load of the vehicles; legal is the heaviest observed
   Answer: A. The legal axle load is a legal limit (about 10.2 t single dual-tyre); the standard axle is the 80 kN (8.16 t) reference for the fourth power law. (Key point: Legal vs standard axle)

2. Which of these is a stress induced in a rigid pavement slab due to temperature and sub-base restraint rather than wheel load?
   A. Interior load stress
   B. Warping stress and frictional stress
   C. Kelly's corner load stress
   D. Bearing stress of the tyre
   Answer: B. Warping stress (temperature difference through the slab) and frictional stress (sub-base restraint) are non-load stresses; Westergaard and Kelly give load stresses. (Key point: Stresses in rigid slab)

3. On what basis is the spacing of contraction joints in JPCP decided?
   A. So that the slab length equals the radius of relative stiffness
   B. So that the dowel bars fit between the joints
   C. So that the friction-induced tensile stress at mid-slab does not exceed the allowable tensile stress of young concrete
   D. So that the slab does not expand into the next slab
   Answer: C. The frictional stress sigma_f = WLf/(2 x 10^4) is limited to the allowable tensile stress S_c, giving L_c = 2 x 10^4 S_c/(W f). (Key point: Contraction joint spacing principle)

4. With W = 2400 kg/m3, f = 1.5 and S_c = 0.8 kg/cm2, what spacing results and what is adopted?
   A. About 44 m, adopt 45 m
   B. About 0.44 m, adopt 0.5 m
   C. About 4.4 m, adopt 4.5 m
   D. About 9 m, adopt 9 m
   Answer: C. L_c = 2 x 10^4 x 0.8/(2400 x 1.5) = 4.4 m, and the practical IRC:58 spacing is 4.5 m. (Key point: Joint spacing calculation)

## Related in Transportation Engineering II

- [Types of rigid pavement; standard axle load](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Afour-rigid-pavement-types-standard-axle) — Transportation Engineering II, chapter 2
- [Cumulative standard axle load; rigid pavement advantages](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Acumulative-standard-axle-rigid-advantages) — Transportation Engineering II, chapter 2
- [Temperature stresses in rigid pavement; dowel bar design](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Atemperature-stress-rigid-dowel-bar-procedure) — Transportation Engineering II, chapter 2
- [Pavement layer functions and rigid pavement joints](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Apavement-layer-functions-rigid-joints) — Transportation Engineering II, chapter 2
- [Plain CC pavement thickness by IRC, 7 m highway](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aplain-cc-pavement-thickness-irc-7m) — Transportation Engineering II, chapter 2
- [Types of stresses in cement concrete pavement](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Arigid-pavement-stresses) — Transportation Engineering II, chapter 2, asked 2×

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