ESDU Engineer

Loads in Circular Frames Due to Floor Loading and Hydrostatic Pressure

ESDU 05003, “Loads in circular frames due to symmetric floor loading”, and ESDU 05004, “Loads in circular frames due to hydrostatic pressure”, were issued in April 2005.

Circular frames are commonly used in the construction of airframes such as pressurised fuselages, missile bodies, long range fuel tanks and in other applications. Frames act to support and stabilise the semi-monocoque structure of which they form a part. They serve also in receiving local loadings and redistributing the forces into the skins of the structure.

Frames used in fuselage construction and other applications are often fitted with a floor structure. The floor structure normally comprises lateral floor beams supporting longitudinal seat rails, with bracing to the lower frame in the form of struts and webs. The floor panels are then supported by this grid of lateral and longitudinal members. Cargo lashing points and other features are often incorporated. The internal forces and bending moments arise from distributed freight loads, passenger seat attachments and other loading actions originating from the floor.

In addition, aircraft cylindrical tanks use circular frames to handle the effects of hydrostatic pressure, arising from accelerated flight or ground conditions. Similar loading actions canbe found in certain ground installations and in non-aeronautical applications.

ESDU 05003 presents four figures which provide the direct and shear forces, moments and shear flow in circular frames arising from uniform floor loading. The figures give the loads in the upper frame and at the intersection of the frame with the floor. The location of the floor is defined by the angle between the top of the frame and the point where the floor meets the frame and curves are provided for six separate floor locations over the range 90° to 165°.

ESDU 05004 presents six figures which provide the direct force, shear force and moments in circular frames arising from hydrostatic pressure.The level of the fluid giving rise to the pressure loading is defined by the angle between the top of the frame and the surface of the fluid and curves are provided for 12 separate fluid levels over the range 0° to 165°.

The curves in all of the figures were derived using the classical energy method of analysis and Engineer’s Theory of Bending on the assumption that the frames are, or may be considered to be, relatively very stiff. Frames may be considered very stiff when located centrally in an arrayof many similar frames, all equally loaded. In addition, it was assumed that the difference between the radius of the shell and the radius of the frame measured to the centroid of the frame section is negligible. (This assumption means that, in ESDU 05004, the total amount fluid in th etank is underestimated slightly and therefore a volume correction factor is employed to take account of this.)

In the case of floor loading, it was also assumed that the flexural stiffness of the frame above the level of the floor is constant around the frame, that the lower frame and the floor beam structure are effectively rigid compared with the frame above, and that the floor loading is symmetrically distributed.

In the case of hydrostatic pressure, it was also assumed that the flexural stiffness of the frame is constant around its circumference, that a continuous or frequent load-carrying attachment exists between the skins/stringers and the frames, and that the stringers provide the principal load-spreading mechanism.

All the while these assumptions hold, the methods are valid and may be expected to give realistic results; if the assumptions cease strictly to hold, the methods become suitable more for initial design purposes.

In addition to the primary loadings, typical fuselage frames carry secondary loadings simultaneously. Examples of secondary loadings include the local redistribution of internal pressure loads at passenger windows and external aerodynamic pressure loads. Similarly, particular frames within a tank may be required to handle the overall supporting loads. These frames carry their share of the hydrostatic loads as well as reacting the overall forces. The effects of additional loads can be evaluated using Data Items Nos Struct 03.06.01 to 03.06.04 and then superimposed appropriately on the effects of floor and hydrostatic pressure loading evaluated using ESDU 05003 and 05004 respectively. Also, where forms of symmetrical floor loading other than the uniform distribution considered in ESDU 05003 arise, or where other loads are present, they can be spread and converted to an equivalent uniformly-distributed floor pressure loading; such a conversion is performed in the worked example in the Data Item.

On the subject of circular frames, ESDU 05002, “Direct and shear forces, bending moments, reacting shear flow and radial displacements in a rigid circular frame due to multiple concentrated loads and couples”, will be issued shortly. The Data Item introduces a Fortran computer program which is, in essence, a computerised version of ESDU Struct 03.06.01 to 03.06.04. As such, the program calculates the direct and shear forces, bending moments, reacting shear flow and radial displacements in a rigid circular frame due to multiple concentrated loads and couples. Up to 100 pairs of radial and tangential applied loads, 100 pairs of x- and y-direction applied loads and 100 applied couples may be specified around the circumference of the frame. The program calculates the forces and displacements induced by the individual applied loads and superposes them to give the total values around the circumference of the frame.

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