---
title: "Types of stresses in cement concrete pavement"
subject: "Transportation Engineering II"
chapter: 2
key: "semester_7/transportation_engineering_ii:rigid-pavement-stresses"
source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/rigid-pavement-stresses
site: BCT Engineering
---

# Types of stresses in cement concrete pavement

Transportation Engineering II · Chapter 2: Highway Pavement

- Asked in: 2082 Baisakh, 8 marks; 2070 Chaitra (old course), 8 marks (asked 2 times)
- Video: [Stresses on Rigid Pavement | Highway Engineering | GATE & ESE 2023 Civil Engineering (CE) Exam Prep](https://www.youtube.com/watch?v=ZUDJ9E2I1OM) — BYJU'S Exam Prep GATE & ESE: CE, ME & XE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/rigid-pavement-stresses
- Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-2

## Question

Discuss various types of stress in cement concrete pavement.

## Short answer

Rigid pavement stresses are wheel-load stresses (Westergaard interior, edge, corner), temperature warping stresses (Bradbury coefficients), frictional stresses, and moisture/settlement/joint stresses. Edge and corner combinations control design and are checked against concrete flexural strength.

## Answer

A cement concrete (rigid) pavement slab resting on the subgrade is subjected to stresses from wheel loads and from changes in temperature and moisture. The types of stress (Westergaard's analysis, IRC:58-2015 for design) are:

#### 1. Wheel load stresses
Caused by the load of the vehicle, treated by Westergaard's theory (slab on a Winkler foundation). Three critical positions:

$$
\begin{aligned} \text{Interior:}\ \sigma_i &= \frac{0.316P}{h^2}\left[4\log_{10}\frac{l}{b} + 1.069\right]\\ \text{Edge:}\ \sigma_e &= \frac{0.572P}{h^2}\left[4\log_{10}\frac{l}{b} + 0.359\right]\\ \text{Corner:}\ \sigma_c &= \frac{3P}{h^2}\left[1 - \left(\frac{a\sqrt{2}}{l}\right)^{0.6}\right] \end{aligned}
$$

where $P$ = wheel load, $h$ = slab thickness, $a$ = radius of the loaded area, $b = a$ if $a \ge 1.724h$ and $b = \sqrt{1.6a^2 + h^2} - 0.675h$ otherwise, and $l$ = radius of relative stiffness:

$$
l = \left[\frac{E\,h^3}{12(1-\mu^2)\,k}\right]^{1/4}
$$

($E$ = modulus of elasticity of concrete, $\mu$ = Poisson's ratio, $k$ = modulus of subgrade reaction.) The edge and corner stresses are the highest, so they control the design (corner cracks develop at the joint corners).

#### 2. Temperature (warping) stresses
The top and bottom of the slab are at different temperatures. During the day the top is hotter and tends to expand, so the slab curls down at the edges; at night it curls up. The self-weight and the subgrade restrain this, giving tensile stresses:

$$
\sigma_{te} = \frac{C\,E\,\alpha\,t}{2}\ \ \text{(edge)},\qquad \sigma_{ti} = \frac{E\alpha t}{2}\left[\frac{C_x + \mu C_y}{1-\mu^2}\right]\ \ \text{(interior)}
$$

where $\alpha$ = coefficient of thermal expansion ($10 \times 10^{-6}$ per $^\circ$C), $t$ = temperature difference between top and bottom, and $C$, $C_x$, $C_y$ = Bradbury's coefficients (functions of slab length/$l$). The hot-afternoon edge warping stress is tension at the bottom; night curling gives tension at the top.

#### 3. Frictional stresses
When the slab contracts due to a fall in temperature or shrinkage, friction with the subgrade resists the movement and causes tension at the middle of the slab:

$$
\sigma_f = \frac{W\,L\,f}{2 \times 10^4}\ \text{kg/cm}^2
$$

where $W$ = unit weight of concrete (2400 kg/m$^3$), $L$ = slab length (m) and $f$ = coefficient of friction (about 1.5). It governs the joint spacing and the steel in the slab.

#### 4. Other stresses
Moisture-warping and shrinkage stresses, stresses due to subgrade settlement and swelling, and stresses at joints.

**Combination for design (IRC:58):** at the edge, summer midday: load + warping − friction, and winter midday: load + warping + friction; at the corner (critical at night): corner load stress + corner warping stress. The critical value is compared with the flexural strength of concrete with a factor of safety (fatigue is also checked).

## Check yourself

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

1. Which wheel load positions in a concrete slab give the highest stresses controlling design?
   A. Interior and centre
   B. Edge and corner
   C. Only the interior
   D. Mid-slab under the dowels
   Answer: B. Westergaard's analysis shows edge and corner stresses are highest, so they control design. (Key point: Critical load positions)

2. The radius of relative stiffness l = [E h^3 / (12(1 - mu^2) k)]^(1/4) depends on:
   A. Slab and subgrade stiffness: E, h, mu and k
   B. Only the wheel load
   C. Only the temperature difference
   D. Only the joint spacing
   Answer: A. l combines the concrete modulus, thickness, Poisson's ratio and the modulus of subgrade reaction. (Key point: Radius of relative stiffness)

3. How do warping stresses arise in a slab?
   A. From the weight of the wheel only
   B. From a temperature difference between top and bottom, with the slab curling and being restrained by self-weight and subgrade
   C. From the friction of the dowel bars
   D. From uniform temperature rise of the whole slab
   Answer: B. A top-to-bottom temperature differential makes the slab curl; restraint produces tensile stress. (Key point: Warping stress)

4. Frictional stress sigma_f = W L f /(2 x 10^4) is caused by:
   A. Slab contraction resisted by the subgrade, giving tension at mid-slab
   B. Wheel load at the corner
   C. Rainfall on the surface
   D. Moisture warping only
   Answer: A. When the slab shrinks, subgrade friction resists movement and causes tension at the middle; it determines joint spacing. (Key point: Frictional stress)

5. For design, the critical stress at the edge is taken as:
   A. Load stress alone
   B. Warping stress alone
   C. Load stress plus warping stress, compared with flexural strength with a factor of safety
   D. Frictional stress alone
   Answer: C. IRC:58 sums the load and warping stress (day or night case) and checks against flexural strength with fatigue. (Key point: Design combination)

## Related in Transportation Engineering II

- [Construction steps of cement concrete pavement](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Acc-pavement-construction-steps) — Transportation Engineering II, chapter 3
- [Rolled vs normal concrete; CC pavement construction](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Arolled-concrete-cc-pavement-construction) — Transportation Engineering II, chapter 3
- [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
- [Bituminous pavement types; asphalt concrete construction](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Atypes-bituminous-pavement-ac-construction) — Transportation Engineering II, chapter 3
- [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
- [Failures of rigid pavement](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Arigid-pavement-failures) — Transportation Engineering II, chapter 4, asked 2×

## Related in other subjects

- [Stress-strain curves, design values of stresses](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Astress-strain-curves-design-values-of) — Design of RCC Structure, chapter 3, asked 4×
- [Stress-strain of paste, aggregate, concrete](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Astress-strain-three-phase) — Concrete Technology and Masonry Structure, chapter 4
- [Rate analysis: plain cement concrete (1:3:4)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Arate-pcc-1-3-4) — Estimating and Costing, chapter 4
- [Theoretical strength of moist cured concrete (1 kg cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Atheoretical-strength-1kg-cement) — Concrete Technology and Masonry Structure, chapter 4