*Problem:*

How do you work out the HA loading and bending moment for a bridge deck ?

*Example: *

Carriageway = 6m wide

Deck span = 34m (centre to centre of bearings for a simply supported single span)

Design for a metre width of deck :

Cl 3.2.9.3.1.

Number of notional lanes = 2

Notional lane width = 6.0/2 = 3.0m

Cl 6.2.1.

Loaded length = 34m

W = 336(1/L)^{0.67} kN/m (per notional lane)

W = 31.6 kN/m (per notional lane)

Cl 6.2.2.

Knife Edge Load = 120 kN (per notional lane)

Cl 6.4.1.1. Table 14.

α_{2} = 0.0137[b_{L}(40-L)+3.65(L-20)]

α_{2} = 0.0137[3.0(40-34.0)+3.65(34.0-20)] = 0.947

Note: For loaded lengths less than 20m the load is proportioned to a standard lane width of 3.65m, i.e. 0.274b_{L} = b_{L}/3.65.

For a metre width of deck :

W = (31.6 x 0.947)/3.0 = 10.0 kN/m

KEL = (120 x 0.947)/3.0 = 37.88 kN

Maximum mid span Bending Moment with KEL at mid span:

M = (10.0 x 34^{2})/8 + (37.88 x 34)/4 = 1767 kNm

Cl 6.2.7.

γ_{fL} = 1.20 (Serviceability limit state - combination 1)

γ_{fL} = 1.50 (Ultimate limit state - combination 1)

Design HA moment for a metre width of deck :

M_{sls} = 1767 x 1.2 = 2120 kNm

M_{ult} = 1767 x 1.5 = 2650 kNm

__Note: Use of γ _{f3}__

BS 5400 Pt.3 & Pt.5 - γ

BS 5400 Pt.4 - γ

Assume the road over the bridge is not a Principal Road then we need to check for 30 units type HB loading (see BD 37/01 Chapter 4).

Cl 6.3.1

Nominal load per axle = 30units x 10kN = 300kN

The maximum bending moment will be achieved
by using the shortest HB vehicle i.e. with 6m spacing (see BS 5400-2:2006 Fig 12).

The maximum moment for a simply supported span occurs under the inner axle
when the vehicle is positioned such that the mid span bisects the distance
between the centroid of the load and the nearest axle.

With a 34m span and the 6m HB vehicle with equal axle loads, the inner axle
is placed at 1.5m from the mid span.

RL = 300(10.7+12.5+18.5+20.3)/34 = 547 kN

RR = 4x300-547 = 653kN

Moment at X = 547x15.5 - 300x1.8 = 7939kNm

Cl 6.4.2

The HB vehicle occupies one lane with HA load in the adjacent lane. Assume for the example that the HB load is carried by a standard lane width of 3.65m.

Hence the moment per metre width of deck = 7939/3.65 = 2175kNm

Cl 6.3.4.

γ_{fL} =
1.10 (Serviceability limit state - combination 1)

γ_{fL} =
1.30 (Ultimate limit state - combination 1)

Design HB moment for a metre width of deck :

M_{sls} = 1.1 x 2175 = __2393__ kN/m (compared to 2120 for HA
load)

M_{ult} = 1.3 x 2175 = __2828__ kN/m (compared to 2650 for HA
load)

Hence in this case HB load effects would govern although a grillage or
finite element type distribution would reduce the HB moment considerably.

Contact David Childs