The structural design of bridge involves the choice of the size and shape and quantity of reinforcement of different members of the bridge to be adequate to bear all the loads coming on them at different conditions. It is important to have a good knowledge of possible loads that a bridge can have in order to do adequate analysis and safe design for the bridge.
The various loads considered in bridge design include:
- Dead loads
- Live loads (Traffic from pedestrian and vehicles)
- Impact loads
- Horizontal thrust on piers and abutments due to flowing water
- Wind loads
- Centrifugal force due to curvature
- Breaking and starting pressures
- Buoyance forces
- Temperature stresses in construction, expansion and contraction joints
- Earth pressure for foundation design
- Deformational stresses
- Construction stresses
- Seismic loads
- Lateral loads
According to Gupta and Gupta (2012), when designing bridges and culverts, any of the combination of forces above that exist should be accounted for. The net stresses should not be allowed to exceed the permissible working stresses. Things to note:
- If temperature stresses are included, the net stresses need to be exceeded by permissible stresses by at least 15% of the net stresses.
- If deformation stresses and construction stresses act in conjunction with temperature stresses, the permissible stresses should exceed net stresses by at least 25% of the net stresses.
- If seismic (earthquake) forces are involved, the permissible stresses should exceed the net stresses by 50% of the net stresses.
- For steel bridges, the stresses should never exceed the yield stress of the steel.
Formulas to determine magnitude of loads in Reinforced Concrete girder bridges:
Dead load: dead load is the load of the structural members of a bridge. It is usually calculated based on the size of the structural members of the bridge and the corresponding unit weight. The span of the bridge is also taken into consideration in the estimation of dead loads. Gupta and Gupta (2012) pointed out that owing to the difficulty in predicting correct dead, it is usually assumed based on two factors:
- The dead load is assumed either on the basis of similar existing structure or assumed on the basis of some empirical formulae
- The dead weight initially assumed should be checked after the design is completed and the design should be revised if the dead weight exceed the assumed dead load by more than 2.5%
Many empirical formulae exist to estimate dead loads and other types of loads but I would tailor the post to that of RCC girder bridges which are among the commonest especially in Nigeria and other developing Nations of the world.
Having decided on the length of each span, the weight of the deck within the span can be determined using
W = 425 + 82 L (for bridges of 6 – 15 m span)
W = 425 + 148 L (for bridges less than 6 m span)
L = length of span (m) and
W = dead weight of span (kgm-2)
Live load: Live loads on bridges are due to vehicles plying the bridge and pedestrians for pedestrian bridges.
For pedestrian bridges,
If span, L ≤ 7.5 m assume Live Load = 400 kgm-2
If 7.5 m ≤ L ≤ 30 m, Live Load = 400 – ((40L – 300)/9)
If L ˃ 30 m, Live Load = (140 + (1400/L)) x ((165 – w)/15)
w = width of the foot bridge
For road bridges, this depends on the different classes of loading as specified by a country’s manual for bridge design.
For railroad bridges, it depends on the gauge track of the bridge and wheel loads of the train.
Impact load: This is due to jumping action of fast moving load on an uneven surface of a bridge. The jumping action produces vibrations. The stresses due to the jumping loads are usually higher than stresses produced by gradual loads. The main causes of impact include:
- Unbalanced weight of the moving vehicles.
- Uneven and rough surface or track.
- Deflection of floor beams and rail bearers.
- Eccentric wheels.
The effect of impact load can be reduced by:
- Increasing the depth of the floor of the bridge.
- Increasing the span of the bridge.
- Reducing the speed of vehicles when crossing bridges.
The impact load is usually estimated as a fraction of the Live load where the fraction represent impact factor.
Impact factor, I = 4.6/(6+L) ≤ 0.5
I = impact factor (if I ˃ 0.5, use 0.5)
Impact load = Live Load x Impact factor (LL x I)
Horizontal thrust due to flowing water
This can be determined using the equation below
P = 52 v2
where v = velocity of flowing water. The value of v2 is assumed to vary linearly from zero at the point of maximum scour to maximum at the free surface. The maximum velocity at the surface is taken as √2 times the maximum mean velocity of the water to calculate the pressure on piers (Gupta and Gupta, 2012).
v is usually gotten from Manning’s or Chezy’s equations found in most hydraulics textbooks
Based on Manning’s formuala,
v = (1/N)m(2/3)i(1/2)
where m = hydraulic mean depth; i = hydraulic gradient and N = roughness coefficient
Based on Chezy’s formula,
v = C√mi or C√RS
where m = R = hydraulic mean depth or radius,
S = slope;
Chezy’s constant, C = 157.6/(1.81+(k/√m))
where k = hydraulic conductivity
The abutment and wingwall of a bridge usually experiences pressure due to backfilled earth. It is necessary to account for this. It is also necessary that proper drainage should be provided for this backfill through the provision of weep holes, pipe drains and gravel drains or else the effect of submerged soil should be accounted for in the design. The earth pressure can be determined using Rankine’s earth pressure equations as follows:
P = (1/2)wh2 cos δ √(cos2δ – cos2ϕ)/(cos2δ + √(cos2δ – cos2ϕ)
where δ = angle of repose (oC)
ϕ = angle of internal friction(oC)
h = thickness of fill material (m)
w = weight of fill material. It is taken as 1600 kgm-3 if not known
Centrifugal force (C.F.)
A bridge structure on curve experiences centrifugal forces due to moving vehicles. It can determined thus:
C.F. = (wv2)/127R
where w = equivalent distributed liveload (kgm-1),
v = velocity (kilometer per hour) and
R = radius of curvature (m)
The thermal coefficient of expansion or contraction of structural components of steel or reinforced concrete can be taken as 11.7 x 10-6 per degree centigrade. For plain concrete it is taken as 10.8 x 10-6. Knowing the change in temperature, its magnitude can be determined.
This can be in the form of shrinkage of concrete, yield in concrete, movement of supports and deformation of members. For reinforced concrete bridges, shrinkage coefficient may be taken as 2 x 10-4.
I refer the reader to consult specialized bridge design and construction textbooks and bridge design manuals of ones country for more on this.
Gupta, B.L. and Gupta, A. (2012). Highway and Bridge Engineering. Standard Publishers Distributors, Delhi, India.