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Using a prestressed Y4 beam with reinforced concrete deck slab as the deck example as shown in Fig.1; the deck having a 10° skew, a span of 20m and carrying a 7.3m carriageway with two 2m footpaths.

BS 5400 Pt.2:2006 Cl.3.2.9.3.1
7.3m carriageway has 2 notional lanes hence lane width = 3.65m.
Cl.6.3 The deck shall carry 45 units of HB
Cl.6.7 Assume bridge requires high containment parapets hence collision loading needs to be considered.

1.HA UDL + KEL

HA UDL can be applied to each longitudinal member as a uniformly distributed load, the intensity of the load is proportional to the width of the lane directly above the longitudinal member, for example:

HA UDL for a 20m span = 45.1kN/m of notional lane.
Notional lane width = 3.65m
HA UDL/m width = 45.1 / 3.65 = 12.36kN/m
HA UDL on member 2 = 0.15 x 12.36 = 1.85kN/m
HA UDL on members 3,4 & 5 = 1.0 x 12.36 = 12.36kN/m
HA UDL on member 6 = 0.5 x 12.36 = 6.18kN/m

UDL applied to each longitudinal grillage member to represent HA UDL in lane 1.

Alternatively, if the program has the facility of applying patch loads then a patch width equal to the lane width and length equal to the loaded length may be applied. The patch load is usually positioned by the centroid of the patch area in relation to the grid co-ordinates.

HA KEL can also be applied as a uniformly distributed load to the transverse members. As loads are initially proportioned to the adjacent members and joints then the worst effects will always be achieved by positioning the KEL directly above a transverse member. If the deck is skewed then the postion of the KEL to give the worst effect will be different to a square deck and two or three positions may need to be checked to find the critical case.

It is therefore useful to separate the HA UDL and HA KEL into different load cases to avoid repeating the calculation for the effects of the UDL. The UDL and the various positions of the KEL can be added together in different combination cases.

Similar load cases are produced for the HA UDL and KEL in the second lane. Full HA live load will have the HA UDL and KEL in both lanes whilst HB live load has the HB vehicle in one lane and the HA UDL and KEL in the second lane. All these variations in load cases can be developed in the combination cases.

The HB vehicle consists of four axles with four wheels on each axle and is applied to the grillage as a series of point loads. Clause 6.3.2 and 6.3.3 allow the wheel loads to be applied as patch loads however there is little to be gained in a global analysis by applying this refinement and point loads will be a suitable representation for the wheel loads.

There are five variations of the inner axle spacing for the HB vehicle that can be applied to the deck. A line beam analysis incorporating moving point loads will indicate the positions of the critical HB vehicle to achieve the design moments and shears. An Excel spread sheet using moment distribution to carry out a line beam analysis of standard moving vehicles can be downloaded by clicking here.

The result of the line beam analysis shows that the maximum sagging moment occurs at 8.5m from the end of the deck with the leading axle at 16.3m from the end.

The result of a line beam analysis shows that the maximum sagging moment occurs at 8.5m from the end of the deck with the leading axle at 16.3m from the end.

All critical load cases are produced from the vehicle with the 6m inner axle spacing.
As the loading is symmetrical and both ends of the single span deck are simply supported then the position of maximum moment can be measured from either end of the deck.

The transverse position of the HB vehicle will depend on which member is being considered, however it is usual to design all internal beams for the critical loading condition for vehicles on the carriageway. The edge beams will require special consideration to support the additional loading from the cantilever.

The diagram shows one of the inner wheels on the critical axle positioned over the nearest transverse member at 8.5m from the support.

This would produce the critical loading condition for the bending moment on the internal beam for an orthoganal deck, however other positions need to be considered to take account of the skew effects.
As a check on the data, the total of the reactions should equal the total load of the vehicle = 4 x 450 = 1800kN. Also the line beam analysis gives a total moment of 5692.5kNm; so as there are four longitudinal members supporting the vehicle, then the moment from the grillage should be in the order of (but less than) 5692.5 / 4 ≈ 1400kNm in the longitudinal member.

Clause 6.5.1 states that the pedestrian live load shall be taken as 5.0 kN/m2, but reduced to 0.8 x 5.0 = 4.0kN/m2 for members supporting both footway and carriageway loading. Consequently the edge beam should be designed for 5.0kN/m2 and the next-to-edge beam designed for 4.0kN/m2. The UDL's can be applied to these two members in a similar manner to the HA UDL described in Section 1. above, however, as there is no barrier between the carriageway and footway, Clause 6.6 requires that the footway members are designed for Accidental Wheel Load which is generally more onerous than the pedestrian live load.

Accidental Wheel Loading consists of a 200kN axle and a 150kN axle with two wheels on each axle and is applied to the grillage as four point loads. Clause 6.6.2 and 6.6.3 allow the wheel loads to be applied as patch loads however there is little to be gained in a global analysis by applying this refinement and point loads will be a suitable representation for the wheel loads.

Similarly as with the HB vehicle a line beam analysis incorporating moving point loads will indicate the critical positions of the vehicle to achieve the design moments and shears. An Excel spread sheet using moment distribution to carry out a line beam analysis of standard moving vehicles can be downloaded by clicking here. The Abnormal Load facility is used in the line beam proforma to input the accidental wheel vehicle.

The result of the line beam analysis shows that the maximum sagging moment occurs at 10.26m from the end of the deck under the leading axle.

The result of a line beam analysis shows that the maximum sagging moment occurs at 10.26m from the end of the deck under the leading axle.

The vehicle will be positioned over the parapet beam as shown to obtain the critical loading condition for bending in this member. This may also be the critical position for the design moment in the main edge beam, however the 100kN wheel should be positioned at joint B to confirm the critical case.

Other positions on adjacent transverse members need to be considered to take account of the skew effects.

As a check on the data, the total of the reactions should equal the total load of the vehicle = 200 + 150 = 350kN. Also the line beam analysis gives a total moment of 1657.5kNm; so as there are two longitudinal members supporting the vehicle, then the moment from the grillage should be in the order of (but less than) 1657.5 / 2 ≈ 800kNm in the longitudinal member.

Loads due to collision with parapets need only be considered in a grillage analysis if high level containment parapets (H4a) are required. Collision loads on other types of parapet need only be considered for local effects (how the load is transferred to the main members).

Clause 6.7.2.1 describes the three loads that are to be applied to the top of the parapet over a 3.0m length.
The point loads need to be transferred down to the datum level of the grillage, which is at the centroid of the deck slab, and distributed over a 3.0m length.
The high containment parapet is 1.5m high above the back of footpath level. The centroid of the deck slab is about 0.3m below the back of footpath level, consequently the two horizontal loads will induce moments on the grillage with a lever arm of 1.8m.

The 500kN horizontal load will produce a moment of 900kNm at the centre-line of the deck. This moment is distributed along a 3.0m length giving 300kNm/m moment to be applied to the grillage.

The horizontal load of 167kN/m will be taken into the deck which, as it is very stiff axially compared to bending, will distribute evenly between all longitudinal members and therefore have negligible effect in the grillage. The load is however considered in determining local effects in accordance with Clause 6.7.1.

The 175kN vertical load can be idealised as a uniformly distributed load 58kN/m along a 3.0m length of the parapet beam.

The 100kN horizontal load acts in the plane of the parapet and there is an argument that the load will be resisted by the framing effect of the parapet rails with the posts and will therefore be transferred to the deck as a series of horizontal and vertical loads at the base of the posts.

As the loads are to be applied over a 3.0m length then the moment of 100kN x (1.5 + 0.3) = 180kNm can be represented by a vertical couple of 60kN x 3.0m.
The horizontal load of 100kN will be taken into the deck which, as it is very stiff axially compared to bending, will distribute evenly between all longitudinal members and therefore have negligible effect in the grillage. The load is however considered in determining local effects in accordance with Clause 6.7.1.