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Therefore the amount of the deformation in any fiber varies directly with its vertical distance from the fiber which remains unchanged in length (Fig. Og). This makes possible the drawing of the strain diagram for the fibers at the section mn (Fig. 9d) which will be a continuous straight line crossing the section at an unknown distance (x) from the top. Experiment has also shown that within the elastic limit of the material there is a fixed relation between strain and stress that stress (pounds per square inch) strain (inches per inch) a constant named the modulus of elasticity (pounds per square inch) or in the usual notation E = 1. It is also true that for timber and steel the modulus of elasticity in compression may be taken as equal to that in tension. It is now possible to draw the stress diagram (Fig. 9e) each abscissa of the strain curve being multiplied by E to obtain that of the stress diagram with the result that it also is a straight line (bcd). The compressive fiber stress on the section, therefore, is represented by the solid seen in side elevation as abc (compare �Fig. 9h) and the tensile force by that projected as cde. Since the total compression equals the total tension, area abc = area dcc.

Since the angles at c are equal ab = de and x = ac = ce = or, in words, the maximum unit compressive stress equals the maximum unit tensile stress and the neutral fiber is at mid-depth. This is a very important fact to keep in mind; that the neutral axis (which is the trace of the neutral plane with the plane of a right section) passes through the center of gravity (or centered) of the cross-section. The resultant compression and the resultant tension evidently act through the cancroids of the triangles by which they are respectively represented and the lever aim of the resisting moment couple equals

a = 23 h. The total compression equals the average compressive unit stress multiplied by the area over which the compression acts; thus G= T=fXbXh and the resisting moment equals MR=G.a=T.a=fXbXhX=*fbh2, which is the familiar expression derived by substituting the values for a rectangular cross-section in the general form of the relation, M=i. The moment of resistance (the couple formed by the internal fiber stresses) developed at any section of a beam equals the bending moment (the moment of the external forces acting on the beam to the right or to the left of the section) at that section, and so the expression BM = MR = *fbh2 gives a direct relation between the maximum fiber stress in a beam and the external loads, making it possible to proportion and investigate rectangular homogeneous beams so far as normal stress is concerned. The problem of shearing stress will be studied later. A beam of plain concrete breaks under very small load on account of the weakness of the concrete in tension. Reinforced with steel rods as shown in Fig. 10 it will carry much more, the concrete cracking at the same load as though unreinforced but failure being prevented by the steel. These cracks usually appear somewhat as shown in the figure, inclined more and more toward the end of the beam.