By Allan G. Bluman
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Additional resources for Math Word Problems DeMYSTiFieD A Self-Teaching Guide
G. the projections on two orthogonal axes x and y. 11 The three-hinged formation six unknowns is determined by setting out the system of three equilibrium equations for any two formations, say I and II. The unknowns thus determined ensure automatically the equilibrium of the third formation also. 12). According to the above, the members of the truss formation will develop exclusively axial forces, and consequently there are three resulting unknowns. 12). The addition of a further node linked to two other nodes of the existing formation, and so on, creates broader statically determinate formations, which can be analysed in the manner described above.
Of course, according to the structural knowledge now available, both these assumptions are false. The concept of the factor of safety for a designed structure can be applied through the theory of plastic analysis, which will be examined later in this book. However, the factor of safety can be practically ensured by means of the following consideration (see Chapters 5 and 6). Let R represent the ultimate resistance (strength) of a designed section in some part of the structure, and let S represent a sectional force of that section corresponding to the load P, under the condition that the equilibrium requirements are satisfied.
The positive senses of the axes N and V as well as of the moment M are chosen arbitrarily. 50 kN m is deduced directly, the negative sign expressing the fact that it is applied in the opposite sense than has been assumed. 85 kN, indicating thereby that it is also acting in the opposite sense. 54 kN may be determined directly. Its sense is again the opposite to what has been assumed. 21). These three magnitudes M, V and N are called the bending moment, the shear force and the axial force, respectively, and constitute the sectional forces at point m.
Math Word Problems DeMYSTiFieD A Self-Teaching Guide by Allan G. Bluman