Box girders are here to stay. In fact today they are taken for granted. Despite this, let us explore whether there can be any shortcomings in the design of a box section for high speed severe duty applications.

All current specifications agree on certain minimum conditions to be fulfilled by the girders in service:

• limiting maximum vertical deflection due to moving live load (SWL and trolley)

• provision of camber in girders (at least to neutralise the dead load deflection)

• limiting combined stresses (sum of stresses due to vertical and lateral moments) – within the calculated allowable stresses.

A missing condition in all specifications is that of limiting the value of maximum lateral deflection that occurs during transient conditions of long travel motion, particularly during braking of the crane. Lateral stiffness of the girders is important. This discussion is valid only for high speed cranes with double flanged wheels (no guide rollers) and a load spectrum 0.8 to 1.

Deflection

Though deflection of a structure is not a measure of its true strength, the layman’s perception is quite the opposite. Excessive deflection gives ‘unsafe’ feelings to the crane user. It might also cause alignment problems in the mechanical drives. During service it is only the vertical deflection due to a moving live load that can be seen, and is measurable. Dead load deflections are not seen since they have already taken a position since installation. Provision of camber has ensured that the trolley runs better, so what remains is to limit the value of vertical live load deflection.

Lateral deflections of girders are unique, occurring during transient conditions of long travel motion. In every cycle they are caused not only by live loads but also by dead loads. For high speed cranes they can be large, particularly during braking. They cannot be measured, they occur in either direction and they can also cause the same alignment problems. The number of times they occur will be much more than vertical ones but, somehow, we have lost sight of this and emphasis has been lacking in limiting lateral deflections, that is emphasis on the lateral stiffness of the box girder.

This stiffness is the resistance to deflection offered by the box girder in the long travel direction and is directly related to the moment of inertia (MI) of the section about the vertical plane (YY axis) usually denoted as Iy; Ix is the MI about the XX axis. We will refer to the ratio Iy/Ix as ‘Ri’. Let Zy and Zx be the corresponding section modulus respectively.

The development history of bridge girders reveals a gradual reduction in the Iy value. Chronological development is shown in Figures 1, 2 and 3.

A reduction in Iy of approximately 30% is estimated in type C compared to A and B. In types A and B the increase in width was to provide enough torsional stiffness to the girder. Combined with the idea of providing a platform on the main frame itself, the width happened to be large, resulting in a high Iy value. When the box section was developed, since the section has a high inherent torsional stiffness, such a large width was not required. The section was, therefore, narrowed down and the platform shifted to cantilever supports outside the main section. That explains why, while the girder weight has increased progressively, lateral stiffness has decreased. This situation is not favourable for high speed cranes and large spans. Let us explore how we can improve on lateral stiffness with little impact on weight.

Design approach

With the current specifications guiding the designer towards vertical stiffness and strength, the box sections are found to be ‘tall’. If we use the word ‘thin’ instead of ‘tall’ we will get the message. Especially, with a centrally located trolley rail, the tendency to reduce on short and long diaphragm weights results in thin girders. (Exceptions are where electricals are housed inside the box and the wide box/monobox design.) Generally the majority of girders would have an Ri value between 0.10 and 0.11. In earlier days this could have been around 0.14 (type A and B). With an Ri of 0.10 the lateral live load deflections, with 10% horizontal loading considered, would be the same as the vertical ones. But in the lateral direction, dead load deflection will not be taken care of. So Ri should be more than 0.10. How to achieve this? Simple, shift the focus: design for Iy. The following example will clarify and two sections are shown in Figures 4 and 5.

Calculations for the properties reveal that both have:

• almost the same Ix and Zx values

• the same allowable stresses

• the same basic section weight (505kg/m).

But the section shown in Figure 5 has 22% more Iy and 11% more Zy. That is, 22% less lateral deflection and 11% less lateral stress. This section is certainly better suited for high speed cranes. The overall girder weight of this section will be only 3% more than in Figure 4 (the incremental weight due to diaphragm and end connections).

This improvement in lateral behaviour has been achieved by making the section wide, or fat, to use a popular term. Thus, the importance of being fat.

End fixity

It may be said that if end connections are made rigid enough, they almost act like fixed ends and thus deflection will be low. True, good end fixity will reduce deflections. But, good lateral end fixity will require large gussets at the four corners, extending well into the girder. This cannot always be provided due to trolley approaches and fear of wire ropes fouling with such gusset plates. Also, for very large spans the efficacy of end fixity is suspect. Hence, it would be wise to provide a basic adequate lateral stiffness in the girder itself and then couple it with maximum possible end fixity.

Deflection impact

Excessive lateral deflection causes abnormal wheel flange wear. Shown in Figure 6 is a scaled down version of an actual crane. For clarity, the deflection of around 30mm is shown exaggerated.

It is suspected that due to lateral deflection a ‘pull-in’ effect is exerted on the end trucks. More deflection means the greater the effect. In Figure 6 f1 and f2 are the imaginary forces due to this effect when the crane is theoretically running centrally and is in braking mode. But, practically, on either side, one of the flanges would always be touching the rail. So, the forces f1 and f2 are translated into reactions at the place where the outer flanges are rubbing the rail. This creates a grinding action at the wheel tread corner, a position that is generally a soft spot, causing wheel flanges to wear out very quickly. It is also suspected that differential deflections skew the end trucks with reference to crane rail axis (the differential force f2 minus f1 or f1 minus f2) adding to the wear problem. Site inspection would guide the user into believing that either the crane is skewing due to drive problems or due to small wheelbase or runway conditions. But this may not be so.

The experience

This article results from a unique site experience with a pair of 35t, 80m/min coil handling cranes in a coil storage bay of a hot strip mill. Investigations into all known parameters that cause excessive flange wear revealed no abnormalities in the running of the two cranes. Dimensions of the cranes, with reference to Figure 6, were: S = 23m; W = 7.5 m; B = 5m; and Ri = 0.11.

As a last resort, almost on a hunch, the possibility of excessive lateral deflection was considered. Rectification work, to improve the lateral behaviour, gave astonishing results: wheel replacements have been nil in the last 15 months, compared with at least twice a month prior to that since commissioning in 1994. Due to the medium span and original Ri value of 0.11, a marginal improvement in Iy value and a good improvement to lateral end fixity gave the results.

But the same approach taken to rectification of 85t capacity, 37m span, 100m/min slab handling cranes with abnormal flange wear, did not yield comparable results, though some improvement was seen. This could be because of the original Ri value being only 0.09 and the span too large (long-travel speeds may have to be reduced). In theory, nothing wrong was noticed in the girder design, fabrication quality, end connections, etc., but the Ri value was observed at around 0.10. This experience led to the realisation of the importance of the ratio Iy/Ix (Ri) and thereby of fat girders.

Logic

For high speed cranes, if 10% is the horizontal force factor, then to limit the lateral live load deflection to the same value as vertical live load deflection, the Iy value has to be a minimum of 10% of Ix value (Ri = 0.1). But as mentioned earlier, in the lateral direction, the dead load deflections have also to be taken care of. So, to restrict this, the Iy value has to be greater than 10% of Ix value (may be between 0.12 to 0.14). This will depend on the value of the lateral dead load deflection.

Conclusion

Limiting the value of total lateral deflection is imperative to arrive at the desired Iy value. Standards and specifications may specify a limiting value, say span/900. Since the lateral deflection is a function of the horizontal force factor (HF), the HFs require a closer look. There are variations in this value in different specifications. HF is expressed as a percentage of vertical loadings. To cite a few: AISE 6: HF = 10% for 50% braked wheels and 20% for 100% braked wheels CMAA: 2.5% min. and further based on acceleration and deceleration FEM: 3% to 30% at wheel based on speed and acceleration Indian Standards specify, depending on class of duty, 5% (M1 to M3), 7% (M4, M5) and 10% (M6 to M8).

So, if HFs can be arrived at more precisely for different speeds, control systems and braking conditions, then the designer will be enabled towards arriving at an optimum section for the intended application. And then the design software may include the Ri value as one of the governing parameters.