Problem:

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

Example:

Carriageway = 7.3m 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 = 7.3/2 = 3.65m

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.

α₂ = 0.0137[b_L(40-L)+3.65(L-20)]
α₂ = 0.0137[3.65(40-34.0)+3.65(34.0-20)] = 1.0
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 1.0)/3.65 = 8.66 kN/m
KEL = (120 x 1.0)/3.65 = 32.88 kN

Cl. 6.2.7.

γ_fL = 1.50 (Ultimate limit state - combination 1)

Design HA loading for a metre width of deck :
W = 1.5 x 8.66 = 12.99 kN/m
KEL = 1.5 x 32.88 = 49.32 kN

Maximum mid span Bending Moment with KEL at mid span = M_ult
M_ult = (12.99 x 34²)/8 + (49.32 x 34)/4
M_ult = 1877 + 419 = 2300 kNm