Estimation of bridge deck design moments

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The deck and girder is one of the commonest type of bridges. In the bridge, girders, which are special beams are used to support the deck slab, where the vehicles move. The deck also includes the road lanes, medians, sidewalks, parapets or railings and other items like drainage and lighting.

The design of the deck and girder bridge begins with the estimation of the design moments both in X and Y-directions. The deck moments would be estimated for both the live loads and the dead loads using the M. Pigeaud’s method. As noted in previous post on functional design, a particular panel is chosen and designed. The panel would cover other panels in the bridge deck. The chosen panel is designed assuming that one of the big/heavyweight vehicles is on the panel. Bridge panels are usually designed as doubly-reinforced sections. Figure 1 shows a given panel showing the vehicle live load.

The M. Pigeaud method deals with the effect of concentrated load on slabs spanning in two directions or on slab spanning in one direction where the width – span ratio exceeds 3.

In the method, the dispersion of the load may be found by the following equation

V = a + 2h

U = b + 2h

With the component terms illustrated in Figures 2 and 3

Where (See Figure 2 and 3)

U = Dispersion of load along the shorter span

V = Dispersion of load along the longer span

a = Dimension of tire contact along the shorter span

b = dimension of tyre contact along the longer span

h = thickness of deck slab (including the wearing course)

Having gotten the values of U and V, the ratio U/B and V/L can be found. The moment coefficients, M₁ and M₂ can be obtained from the M. Pigeaud curves when the values of U/B, V/L and K are known

Note that K = span ratio = B/L, B = Shorter span of the bridge and L = longer span of the bridge

NB: The picture quality of the chart is really poor. You can look for clearer picture to aid your solution

If K ˂ 0.5, assume K = 0; If K ≥ 1, use K = 0.9

Most times, a = 3 m and b = 1.5 m

The moment to be used in design = coefficient of moment from M. Pigeaud chart x 100

Note: where a given correspondence of V/L and U/B does not fall on any of the curve, do interpolation or use a higher value

Moment about Longer span, M_L = P (M₁ + µM₂)

Moment about shorter span, M_B = P (M₂ + µM₁)

Where µ = Poisson’s ratio = 0.15 for reinforced concrete bridges and P = liveload/wheel load of the bridge

The design of bridge span is usually per metre as B is usually 1 m as it is adopted in normal slab design

Note: multiply the final moments by 1.5 (Limit State factor)

For vehicle bridges, Thickness of deck ≥ 160 mm

For Pedestrian bridges, thickness of deck ≤ 120 mm

Example

Assuming a bridge have a span, L = 30 m, Breadth, B = 15 m. if a = 5 m and b = 2.5 m and h = 0.2 m and P = 265 kgm^-2 = 2.6 kNm^-2, determine the design moments.

Solution

K = B/L = 15/30 = 0.5

V = a + 2h = 5 + 2 (0.2) = 5.4 m

U = b + 2h = 2.5 + 2 (0.2) = 2.9 m

V/L = 5.4/30 = 0.18; U/B = 2.9/15 = 0.19

From M. Pigeaud chart, the moment coefficients are

M₁ x 10² = 22.3 x 10² = 2230 kNm

M₂ X 10² = 10 x 10² = 1000 kNm

Short span moment, M_B = P (M₁ + µM₂) = 2.6 (2230 + 0.15 (1000)) = 6188 kNm

Long span moment, M_L = P (M₂ + µM₁) = 2.6 (1000 + 0.15 (2230)) = 3470 kNm

Factored moments, M_B = 1.5 x 6188 = 9282 kNm; M_L = 1.5 x 3470 = 5205 kNm

Design of section is done using respective formulas in limit state

Notes on design of beams

1. Length of longitudinal beam for design is the same as length of the span
2. Length of transverse beams is same as width of span
3. Longitudinal beams can be as low as 35 cm depth
4. Thickness of main longitudinal beams should be between 40 to 60 cm