Skew geometry

• 2025-04-18: Initial version

Skew geometry gets complicated! Archie-M versions through to 2.6 provided rudimentary support for skew geometry in circular segment arches only. From version 2.7, skew support is more complete, and the UI makes clear where Archie-M cannot help with skew geometry (namely with pointed and true shape arches).

To understand skew geometry it is necessary to think about the process of building masonry bridges. The geometry of the intrados (inner or lower surface of the arch) is defined by the timber centring over which the arch is built. For a skew bridge, the centring would be set out either skew (ie aligned with the elevations of the bridge, and thus not perpendicular to the abutment or pier faces) or square (ie perpendicular to the autment and pier faces). There are good reasons to choose each:

• Skew centring minimises the number of centres needed, and makes sense if the bridge is a "one off" so the centres are built for the purpose.
• Square centring fixes the geometry perpendicular to a transport corridor passing under the bridge. It requires additional centres for a given bridge, but these will be available if a large number of bridges were being built over a canal or railway.

When assessing a skew bridge, it is important to consider which way the centres were set. This is the direction on which the geometry was defined. On any other line, the geometry will be modified by the skew.

The ring thickness, meanwhile, is generally defined on the normal to the intrados. With a brick arch, this is a natural result placing bricks on the timber lagging over the centres: the ring will be a multiple of the brick course thickness on the normal to the lagging. So regardless of the orientation of the centres, the ring thickness is defined on the square line.

When assessing a skew bridge, we need to be clear about several things:

• Which way were the centres set.
• For each measurement that would be different on the skew and square lines, which way was it taken.
• Which line do we want to assess on.
• What is the skew angle.
• Which measurements does Archie-M adjust for you.

The measurements that are skew-dependent are:

• Span - the span given to Archie-M must be the span of the centre. If the bridge was measured on the skew line, but has circular geometry on the square line, convert the span to the square span before setting it in the Archie-M model.
• Ring thickness except at the crown - Ring thickness is quite likely to be measured on the skew line (at the elevation), but is always input to Archie-m on the square line, so you may need to make a correction.
• Pier and abutment thickness - these are not modified by Archie-M, you must adjust them for skew yourself as needed.

The skew settings required by Archie-M are:

• A skew angle.
• Which skew transform to apply: square to skew, or skew to square.

The skew transform is the transform from the direction in which the centres were set, to the direction for assessment. The wording has been changed in Archie-M 2.7 to make this clearer.

The square to skew transform will increase the span. Skew to square will reduce it. Change of the span without changing the rise also changes the nature of the shape, so a circular segment becomes segment of an ellipse.

If you wish to assess in the direction of the centres, regardless of whether they were set skew or square, the skew angle should be zero (skew transform disabled). If the centres were set skew and assessment is on the skew line, it may be legitimate to enhance the springing ring thickness, but Archie-M cannot do this for you.

Limitations to be aware of:

• The same skew settings are applied to all spans in multi-span structures, spans with different skew cannot currently be modelled this way.
• No skew transform is applied to the pier or abutments widths, you will need to adjust these yourself.
• Skew angles greater than 60 degrees are not supported.
• Skew transforms are not currently available for pointed or true shape arches.