Structural Theory and Analysis by J. D. Todd (auth.)

By J. D. Todd (auth.)

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The absolute maximum value of the shear force, that is, the maximum value that can occur at any point of the beam, will always be at one of the supports for a simply supported beam. Consideration of the shear-force envelope discussed below will confirm this. 34 the influence line was drawn for point C. There is a unit change in the value of the shear force at this point. The influence line for a point next to the support A would be a triangle of unit negative value at A and zero at B. Similarly for a point at B we should have a triangle with unit positive height at B.

1 Oc shows two smaller roof trusses, each consisting of half the span, again interconnected by three members. 1 0. 1 Oa: This problem can be started by resolving at A then D. Difficulties will arise however if we now attempt to resolve at C-five members meet at this point, and the forces in only two of these have so far been found. If a section is put through as shown, the forces in EG and FH and CH can be found. It is now possible to return to C and resolve as only two unknowns remains. The rest of the analysis can then proceed.

This can be seen by applying the triangle of forces. The resultant of P 1 and P 2 is R 12 , which when combined withP 3 givesP4 . We must note at this stage that the construction gives the magnitude and direction of the resultant, but will not give the point of application, unless it so happens that all the forces pass through a single point. To find the point of application a further construction is required known as the funicular or string polygon. 21a and b. Any point 0 is chosen on the force polygon diagram, this is known as the pole.

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