By E. W. Parkes
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Extra resources for Braced Frameworks. An Introduction to the Theory of Structures
We find P A B = - 0 · 6 χ £ χ 2 4 χ V2/3 = -3-4MN. If the distributed load is not sufficiently long to cover the whole of the positive or negative areas of the influence line, it is necessary to find the position of the load for maximum force in the member. For a simple uniformly distributed load, the maximum occurs when the ordinates of the influence line at either end of the load are equal 54 STATICALLY DETERMINATE TRUSSES \ (a) 0-6 MN/m "»KI/N/fN^ [* 36m /^f0-6x-^ x 3 6 x ^ = +7·6 ΜΝ per unit load 0-6 MN/m ^ΗΆ\\/Κ\/^ 1 i--24m-H 3 (b) B= -0-6x^x24x^1 = -3·4 ΜΝ per unit load FIG.
All of the equations do not have to be solved simultaneously—the tension coefficients can usually be found by solving small groups of equations in turn. Once the tension coefficients have been found, the 42 STATICALLY DETERMINATE TRUSSES forces in the bars can be determined by using equations (13) and (14). We give an example below. Consider the cantilever frame shown in Fig. 30, which is subjected to a load of 15MN at its tip. The positive directions of the coordinate axes are shown in the diagram, and the true lengths of the 5 MN Member True length (m) 42-43 46-37 42-43 30-82 6403 46-37 22-36 30-82 36-74 AF AH BF CH DG DH FG FH GH FIG.
As an example we may consider the frame of Fig. 30, where there are nine bars, twelve reactive forces and seven joints: equation (20) is satisfied and the structure is statically determinate. 47 BRACED FRAMEWORKS We may summarise the formal conditions for statical determinacy as follows : (1) The shape of the framework must not change significantly throughout the range of its environment. (2) The number of bars (b), reactive forces (r) and joints (j) must be related by the equation b + r = 2j (plane frame) 3/ (three-dimensional frame) (3) The bars must be properly arranged.
Braced Frameworks. An Introduction to the Theory of Structures by E. W. Parkes