The Structural Engineer's Corner

Eng. Onorio Francesco Salvatore

Traffic loads on road bridges: division of the carriageway into notional lanes according to Australian Standard 5100.2

Written By: Lexatus - Nov• 14•13

Traffic loads 16 - Onorio

The load models defined in the Australian Standard 5100.2 shall be assumed to occupy one standard design lane of 3.2 m width. The number of standard design lanes is defined as:

n = b / 3.2 (rounded down to next integer)

where:

n = number of standard design loads;

b = width between traffic barriers, in metres, unless specified otherwise.

The Code standard design lanes shall be positioned laterally on the bridge to produce the most adverse effects.

For multiple lanes, the A160, M1600 or S1600 loading shall be multiplied by an accompanying lane factor as follows: (more…)

Traffic loads on road bridges: a practical example

Written By: Lexatus - Nov• 12•13

Traffic loads 15 - Onorio

After the recent posts on the traffic loads as defined by EN 1991-2, let’s make an example. We have a bridge covering a span of 50.0 m with a static scheme of simple abutment. The roadway is 7.50 m wide flanked on each side by walkways having a width of 2.0 m. The walkways are separated from the central road by safety barriers.

The first step is to define the width w of the roadway and the number of notional lanes, in accordance with the EN 1991-2 “Actions on structures. Part 2: general actions – Traffic loads on bridges“.

The walkways are accessible only to pedestrians, hence the width w is delimited by the net distance between the aforeside guardrails.

Being the roadway 7.50 m, hence w > 6.0 m, the number of conventional lanes is: (more…)

Traffic loads on road bridges: the Load Model 4 (LM4) in Eurocodes

Written By: Lexatus - Nov• 12•13

Traffic loads 11 - Onorio

The Load Model 4, as defined in the EN 1991-2, is the crowd loading and is represented by a UDL equal to 5 kN/m². It includes dynamic amplification and in certain cases can be more critical than LM1.

It has been found that LM4 > LM1 in the following cases: (more…)

Traffic loads on road bridges: the Load Model 3 (LM3) in Eurocodes

Written By: Lexatus - Nov• 11•13

Traffic loads 10 - Onorio

Some road bridges must be designed against special traffic loads. This is the case of bridges that may experience a military use during their lifetime. The very conventional model used represents special vehicles that can exceptionally transit on bridges as abnormal vehicles. The application can concern one or several special vehicles. This case is detailed in the Annex A of EN 1991-2 which defines standardized models of special vehicles whose total weight ranges from 600 to 2400 kN. (more…)

Traffic loads on road bridges: the Load Model 2 (LM2) in Eurocodes

Written By: Lexatus - Nov• 10•13

Traffic loads 9 - Onorio

The Load Model 2 (LM2) is a single axle model, which is applied when a local verification for short structural elements is required. Such elements can be crossbeams, upper flange stiffeners of othotropic decks or deck panels of composite slabs with steel sheeting. The internal forces due to LM2 may then be more critical compared to those of LM1. This can also happen at the vicinity of the expansion joints.

LM2 is applied at any location of the carriageway and consists of a single axle load with a magnitude equal to βQ x Qak, where βQ is an adjustment factor whose value may be defined in the National Annex. The EN 1991-2 recommend:

βQ x Qak = αQ1 x Qak = 400 kN

However, (more…)

Traffic loads on road bridges: the Load Model 1 (LM1) in Eurocodes

Written By: Lexatus - Nov• 10•13

Traffic loads 6 - Onorio

As discussed in the previous post, the Load Model 1 should be used for both global and local verifications. It is intended to cover flowing, congested or traffic jam situations with a high percentage of heavy lorries. In general, when used with the basic values, it covers the effects of a special vehicle of 600 kN.

The Load Model 1 consists of two partial systems:

– Double axle concentrated loads, called Tandem System (TS), with weight αQi x Qk per axle;

– Uniformly distributed loads (UDL), with weight αqi x qik.

Should be noted that: (more…)

Traffic loads on road bridges: the Traffic Load Models

Written By: Lexatus - Nov• 10•13

Traffic loads 2 - Onorio

In the Eurocodes there are four Traffic Load Models to be used for the determination of road traffic effects associated with Ultimate Limit and Serviceability Limit States.

These load models for vertical loads represent different traffic effects. In short:

LOAD MODEL 1 (LM1): (more…)

Traffic loads on road bridges: division of the carriageway into notional lanes according to Eurocodes

Written By: Lexatus - Nov• 10•13

Traffic loads 1 - Onorio

In this post we’ll discuss about the traffic loads on road bridges according to Eurocodes.

The first step when evaluating the loads is the division of the carriageway into notional lanes. The width of the carriageway (w) has to be measured between the inner limits of vehicle restraint systems. Should not be included in the width:

– the distance between fixed vehicle restraint systems;

– kerbs of a central reservation;

– widths of the vehicle restraint systems.

The width, taken as per above, should then be divided into notional lanes. The width of the notional lanes and their number is defined accordingly to the Code instructions. (more…)

The coefficient of earth pressure at rest, K0

Written By: Lexatus - Oct• 29•13

Coefficient of earth pressure at rest 15 - Onorio

When dealing with geotechnical problems often is required that the initial stress state in the soil has to be known. In order to define the initial state at rest, the coefficient K0, called coefficient of earth pressure at rest, has to be calculated.

The best way I could think about to explain this coefficient is to have an analogy with the water. Let’s consider a swimming pool: the pressure on the wall at a specific depth y is given by the specific weight of the fluid multiplied by the depth. In reality, in this way we have found the vertical pressure, but because in a fluid such as water the pressure is the same in all directions, we have found also the horizontal pressure. (more…)

Hydrodynamic effects during earthquakes on dams and retaining walls: Zangar’s theory

Written By: Lexatus - Oct• 27•13

Zangar for dams 3 - Onorio

In this post we’ll study the Zangar’s theory for dams and retaining walls, following the previous posts on the same subject where we went through the theories of Westergaard (“Hydrodynamic effects during earthquakes on dams and retaining walls: Westergaard’s theory“) and von Karman (“Hydrodynamic effects during earthquakes on dams and retaining walls: von Karman’s theory“).

Zanagar proposed an Electric analog with the problem studied by Westergaard (“Electric analog indicates effect of horizontal earthquake shock on dams“, Zangar, C. N. & Haefeli, R. J. – Civil Engineering, April 1952). Zanagar referred to the same assumptions made by Westergaard (rigid dam, small displacements, plane motion, infinite reservoir) by neglected the compressibility of the water (similarly to von Karman). He found that the differential equation for the pressure gets the shape of the Laplace’s equation, that relates to the flow of an electric current. Zangar found a solution through the nominal values of the equipotential lines intersecting the dam. (more…)