Joints solve one problem and create another. Cutting a concrete pavement into separate slabs relieves temperature stresses — but it also means a wheel arriving at the joint drops onto a slab edge with nothing supporting it from the other side.
Dowel bars solve that. This post covers what they do, the three ways they can fail, and the five-step design procedure.
What Dowel Bars Do
- Dowel bars act as load transfer devices across transverse joints.
- They keep the two slabs at the same height.
- They are mild steel round bars, bonded on one side and free on the other side.
Why One End Must Be Free
This is the detail that makes a dowel bar work, and it is worth understanding rather than memorising.
If a bar were bonded into both slabs, it would tie them together and prevent the joint from opening and closing — which defeats the entire purpose of having a joint at all. The temperature stresses would return.
By bonding only one end, the bar can slide freely in the other slab. The joint stays free to open and close with temperature, while the bar still carries vertical load across the gap. It transfers load without transferring movement.
Standard Dimensions
| Property | Range |
|---|---|
| Diameter | 25 mm to 40 mm |
| Length | 400 mm to 500 mm |
| Material | Mild steel, round bars |
Stresses in the dowel bar are given by Bradbury’s analysis.
Three Ways a Dowel Bar Can Fail
A dowel bar spanning a joint is loaded in three distinct ways, and each gives its own load transfer capacity.
1. Load Transfer Capacity in Shear
Ps = (π / 4) d2 σs
| Symbol | Meaning |
|---|---|
| Ps | Load transfer capacity of dowel bar in shear |
| d | Diameter of dowel bar |
| σs | Permissible shearing stress in steel |
This is the simplest of the three — the cross-sectional area of the bar multiplied by the permissible shear stress. Shear failure would mean the bar is sliced through at the joint face.
2. Load Transfer Capacity in Bending
Pb = 2 d3 σb / (L + 8.8δ)
| Symbol | Meaning | Unit |
|---|---|---|
| Pb | Load transfer capacity in bending | kg |
| d | Diameter of dowel bar | cm |
| σb | Permissible bending stress in dowel bar | kg/cm2 |
| δ | Gap of joint | cm |
| L | Embedded length of dowel bar | cm |
Bending failure means the bar bends within the joint gap. Note that a wider joint gap δ reduces the capacity, because the unsupported span of the bar increases.
3. Load Transfer Capacity in Bearing
Pbearing = σbr L2 d / [ 12.5 (L + 1.5δ) ]
| Symbol | Meaning |
|---|---|
| Pbearing | Load transfer capacity in bearing, kg |
| L | Embedded length of dowel bar, cm |
| d | Diameter of bar, cm |
| δ | Gap of joint, cm |
| σbr | Permissible bearing stress |
Bearing failure is different in nature from the other two — it is the concrete that fails, crushed by the bar pressing against it, rather than the steel. This is why the embedded length appears squared: a longer embedment spreads the bearing pressure over more concrete.
Comparing the Three
| Mode | What Fails | Depends Most On |
|---|---|---|
| Shear | Steel, sliced at the joint | d2 |
| Bending | Steel, bent across the gap | d3 and joint gap |
| Bearing | Concrete, crushed by the bar | L2 and d |
The Five Design Steps
Step 1 — Find the Embedded Length
The embedded length is decided by equating strength in bending and bearing. At this stage the joint width δ and the dowel diameter d are assumed.
L = 5d √[ σb(L + 1.5δ) / (σbr(L + 8.8δ)) ]
Note that L appears on both sides — this equation must be solved by trial, assuming a value of L, substituting, and iterating until both sides agree.
The logic of equating bending and bearing is economic. If bending capacity were much lower than bearing capacity, the steel would fail first and the extra embedment would be wasted. Setting them equal gives the most efficient bar.
Step 2 — Find the Load Transfer Capacities
Compute Ps, Pb and Pbearing using the three formulas above.
Step 3 — Establish the Design Basis
The load transfer capacity of the dowel bar system is assumed to be 40 percent of the wheel load.
The distance on either side of the load position up to which the group of dowel bars is effective in load transfer is taken as 1.8 l, where l is the radius of relative stiffness.
Two important ideas here.
First, the dowels do not carry the whole wheel load — only 40 percent needs to be transferred across the joint. The rest is carried directly by the loaded slab.
Second, load is shared by a group of bars, not just the one directly beneath the wheel. Bars within 1.8 l on either side all contribute. Once again the radius of relative stiffness governs, as it has throughout rigid pavement design.
Step 4 — Load Capacity Factor Required
Required factor = maximum of ( 0.4P/Ps , 0.4P/Pb , 0.4P/Pbearing )
where P is the wheel load.
Each ratio asks: how many bars’ worth of capacity does this failure mode demand? The maximum of the three governs, because the system must be safe against all three modes simultaneously — and the weakest mode is the one that decides.
Step 5 — Load Capacity Available from the Group
The capacity factor of a dowel bar is assumed to be 1 just below the wheel, and zero at a distance of 1.8 l from the wheel.
Load capacity = 1 + (1.8l − δ)/1.8l + (1.8l − 2δ)/1.8l + (1.8l − 3δ)/1.8l + …
continuing so long as the numerator remains positive
Here δ is the spacing between dowel bars.
Reading This Series
The idea is a linear drop-off. The bar directly under the wheel contributes fully, a factor of 1. Each successive bar is further away and contributes proportionately less, falling linearly to zero at 1.8 l.
So the first term is 1, the second is the bar at distance δ, the third at 2δ, and so on. You keep adding terms until a numerator turns negative — meaning that bar lies beyond 1.8 l and contributes nothing.
The spacing δ should be chosen such that the load capacity available is greater than the load capacity factor required.
And finally:
Actual length of dowel bar = L + δ
The bar must be embedded a length L in each slab, plus it must span the joint gap.
The Whole Procedure at a Glance
| Step | Action | Key Relation |
|---|---|---|
| 1 | Find embedded length by equating bending and bearing | L = 5d√[σb(L+1.5δ)/(σbr(L+8.8δ))] |
| 2 | Compute the three capacities | Ps, Pb, Pbearing |
| 3 | Set design basis | 40 % of wheel load; effective zone 1.8 l |
| 4 | Find required capacity factor | max(0.4P/Ps, 0.4P/Pb, 0.4P/Pbearing) |
| 5 | Choose spacing so available capacity exceeds required | Series summed to 1.8 l |
Formula Summary
| Quantity | Expression or Value |
|---|---|
| Capacity in shear | Ps = (π/4)d2σs |
| Capacity in bending | Pb = 2d3σb/(L + 8.8δ) |
| Capacity in bearing | Pbearing = σbrL2d/[12.5(L + 1.5δ)] |
| Embedded length | L = 5d√[σb(L + 1.5δ)/(σbr(L + 8.8δ))] |
| Load transferred | 40 % of wheel load |
| Effective distance | 1.8 l on either side |
| Actual bar length | L + δ |
| Dowel diameter | 25 to 40 mm |
| Dowel length | 400 to 500 mm |
Quick Revision Notes
- Dowel bars are load transfer devices across transverse joints and keep the two slabs at the same height.
- They are mild steel round bars, bonded on one side and free on the other.
- The free end lets the joint open and close while still transferring vertical load.
- Diameter 25 to 40 mm, length 400 to 500 mm.
- Stresses are given by Bradbury’s analysis.
- Three capacities: shear (πd2σs/4), bending (2d3σb/(L + 8.8δ)), bearing (σbrL2d/[12.5(L + 1.5δ)]).
- In bearing, it is the concrete that fails, not the steel.
- Embedded length found by equating bending and bearing strength, solved by trial.
- Dowel system transfers 40 percent of the wheel load.
- Bars within 1.8 l on either side participate; capacity factor is 1 under the wheel and 0 at 1.8 l.
- Actual bar length = L + δ.
Mistakes Students Commonly Make
- Bonding the bar at both ends. One end must be free to slide, or the joint cannot function.
- Using d2 in the bending formula. Bending uses d3.
- Swapping the constants. Bending has 8.8δ; bearing has 1.5δ.
- Forgetting the 12.5 in the denominator of the bearing formula.
- Taking the minimum instead of the maximum of the three ratios in Step 4.
- Using the full wheel load instead of 40 percent of it.
- Assuming only the bar under the wheel carries load. A group within 1.8 l participates.
- Reporting the embedded length L as the bar length. The actual length is L + δ.
- Trying to solve the Step 1 equation directly. L appears on both sides, so it requires trial and iteration.
Conclusion
Dowel bars let a jointed concrete pavement behave as though it were continuous — carrying load across the gap while still allowing the slabs to move with temperature. The design balances three failure modes: shear and bending in the steel, and bearing in the concrete. Equating bending and bearing fixes the embedded length, the worst of the three ratios fixes the required capacity, and the spacing is then chosen so that the group of bars within 1.8 l supplies more capacity than is demanded. Remember that only 40 percent of the wheel load has to cross the joint, and that the bar’s actual length is L + δ.
Frequently Asked Questions
What is the function of a dowel bar?
To act as a load transfer device across transverse joints and to keep the two adjoining slabs at the same height.
Why is a dowel bar bonded on only one side?
So that the joint can still open and close with temperature change. If both ends were bonded, the bar would tie the slabs together and the joint would be unable to function.
What are the standard dimensions of dowel bars?
Normally 25 mm to 40 mm in diameter and 400 mm to 500 mm in length, made of mild steel round bars.
Whose analysis gives the stresses in dowel bars?
Bradbury’s analysis.
What are the three load transfer capacities?
Capacity in shear, Ps = (π/4)d²σs; capacity in bending, Pb = 2d³σb/(L + 8.8δ); and capacity in bearing, Pbearing = σbrL²d/[12.5(L + 1.5δ)].
What fails in the bearing mode?
The concrete, which is crushed by the bar pressing against it, rather than the steel bar itself.
How is the embedded length determined?
By equating the strength in bending and in bearing, giving L = 5d√[σb(L + 1.5δ)/(σbr(L + 8.8δ))]. Since L appears on both sides, it is solved by trial.
How much of the wheel load do dowel bars transfer?
40 percent of the wheel load.
Over what distance are dowel bars effective?
1.8 l on either side of the load position, where l is the radius of relative stiffness.
How is the load capacity factor calculated?
As the maximum of 0.4P/Ps, 0.4P/Pb and 0.4P/Pbearing, since the system must be safe against all three failure modes.
What is the actual length of a dowel bar?
The embedded length plus the joint gap, that is L + δ.