The function of the Deltic's underframe is to support the weight of all components excluding bogies, and to transmit these loads to the bogies. Secondly, it needs to hold all of these components in their correct relative positions. Or in other words, it needs to be sufficiently stiff not to flex too much, which might induce vibrations and fatigue failures on the bodywork. It also needs to achieve the above criteria without being too heavy.
Most of the loading on the underframe is vertical bending, supporting the power-units and boiler in the middle, and various other equipment in each nose end. The bending strength and stiffness is largely achieved by a pair of longitudinal members, fabricated from separate steel plates. These two members are quite close together, to give clearance to the wheels when negotiating tight curves. As can be seen in the illustration below, these members are of very deep section along the engine room. This is where the bending moments on the frame are highest.
Once the underframe has had the body and all components installed, it will have deflected (i.e sagged!) noticeably. To minimise this sagging, the underframes were built with a slight upward camber (i.e. bowed upwards), so that the centre was raised by 1 inch relative to the bogie pivot centres. During bodywork construction, a procedure was followed using ballast weights to straighten the frame, to try and prevent diagonal creases from appearing in the body, distortion of the body frame, and undue stresses on welds, after completion of the loco.
The procedure was revised as experience was gained. A November 1960 revision (ref. 1) specified that the underframe should be supported on special compensating beams at each end. Each of these beams was free to rock on a fulcrum, which became the effective support points for the underframe. Evenly distributed ballast weights were to be used to straighten the underframe until the camber was reduced to 0.25 inch, while the body framing was constructed. Then, while panelling the body, two 8 ton ballast weights were utilised, as shown in the diagram below. These were positioned intitially at 123 inches from the loco centre-line, and then moved as required until the underframe was straightened out fully.
You might think that a pair of 8 ton weights are rather light, considering that the power units in a Deltic weigh 11 tons each, and the finished loco super-structure weighs in at over 50 tons. This is partly because these weights are positioned close to the centre of the loco, and partly because on the finished loco, the weight of the noses has the effect of reducing the bending moments in the engine room region. Also, the compensating beams extend the distance between where the underframe is supported. Published photos suggest that the compensating beams might not have been employed throughout the production run, but ballast weights can be seen. See "Deltics at Work" by Allan Baker and Gavin Morrison (page 20), and "Deltics Super-Profile" by R. M. Tufnell (page 30).
This system of cambering, appears to have neglected the effect of the weight carried at each nose end on the relatively thin framing that passes over the bogies. The bending moments on the underframe reverse in direction near the cab doors as a result. During their service lives, Deltics developed diagonal creases in the panelling next to each cab door. One also has to keep in mind that over a period of time, a permanent 'set' will develop in the structure, after supporting so much weight. That is, the loco sags with age! Flexing up and down of the cab/nose ultimately led to cracking of the bodywork around the windows.
With the underframe ballasted as described above, the maximum bending moments occur along the central length of frame between the two weights. Maximum bending moments equals the horizontal distance between one of the weights and the nearest fulcrum, multiplied by the weight. The fulcrums of the compensating beams were 296.5 inches from the loco centre:
8 x (296.5-123) = 1388 ton-inches (or 116 ton-feet)
If the weights are moved closer together, then the calculated figure could be anything up to 180 ton-feet (the above calculation ignores the weight of the underframe itself, since the 1 inch as-built camber occurs under its own weight). A rough estimate of this figure for the completed loco, suggests that it is somewhere in between those two figures. Add fuel and water, and the loco is likely to sag a little.
1) Vulcan Foundry drawing no. P3258M082
Illustrations are by the author.