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Roofs protect the interiors of buildings against rain, snow, wind, and variations of temperature. The roof may be subjected to adverse temperatures, humid or aggressive conditions or fire hazards. It may be used for parking, storage, as a viewing platform, accessway or roof garden. Access for maintenance is required to all roofs and to any ventilation-type equipment and roof lights. Flat roofs usually have self-draining falls to gutters and discharge systems adequate to remove accumulating water before unacceptable loads or bypassing of the weatherproofing results. Thus precautions to avoid blocking of the drainage system are essential, and the degree of fall must allow for elastic and creep deflections and construction tolerances.
Some of the long-standing teaching problems in structural engineering degree courses are associated with the principle of virtual work. This paper presents a simple proof of the principle for a general deformable body. The proof, which is sufficiently simple for undergraduate teaching, is based on two simple results in engineering mechanics and the exploitation of the concept of virtual displacements to include the use of physically impossible displacements. It is hoped that the paper will contribute towards the teaching of the theory of structures in the universities and polytechnics, and help to remove the misunderstanding of the principle of virtual work which is, at present, widespread among structural engineering students.
F.K. Kong, J.M. Prentis and T.M. Charlton
Since publication of the paper in The Structural Engineer, I have received a letter from Lord Baker, drawing attention to the statement ‘Plastic analysis was developed from research work carried out at Cambridge’. He pointed out, quite rightly, that it was plastic design that was developed and that plastic analysis formed only part of the new concept.