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Aviation History
1941
1941 - 0956.PDF
APRIL 24TH, 1941. Max. Zo 1 No. 182 N the summation of direct and PPrincipal direct stress = Maximum shear stress = •"4 E AIRCRAFT ^ ENGINEER 16th Year COMPOUND STRESS, DIAGRAM Summation of Direct Stresses and SlyKir Stresses Facilitated By W. F. tress, the equations, and are frequently met with by those dealing with stress calculations. In the above formulae p represents the direct stress applied to an element of a material, which may be due to direct tension or compression or to bending, and q represents the shear stress due to direct shear or to torque. The accompanying diagram considerably simplifies the above summation and enables one to visualise how these maximum stresses vary with the ratio of the shear stress to the direct stress. Explanation of the Diagram On a basic circle of 0.5 radius, drawn to any convenient scale, the tan gential perpendicular line is drawn. This is graduated to the same scale as that to which the circle is drawn and on the accompanying diagram has subdivisions of 0.01. This scale represents the ratio—shear stress/direct stress Around a portion of the basic scale, arcs are drawn to intersect the tangential perpendicular mentioned above. These are drawn with radii to the same scale as that of the basic circle. As shown the interspaces each represent 0.02, subdivided into 0.01. Any further subdivision of both the above scales may be done by eye On the arcs it will be noted there are two scales, one for the maximum direct stress and the other for the maximum shear stress. These values, it will be seen below, are factors giving these stresses in terms of the applied direct stress. To Use the Diagram Having determined the applied direct and shear stresses, find the ratio of the latter to the former, i.e.—express the shear stress in terms of the direct stress. Look up the value found on the shear stress/direct stress scale. Note the arc (or intermediate arc if it were drawn) which intersects the perpendicular at this value. Read off the factor on this arc, looking under the appropriate heading " Max. Direct Stress " or " Max. Shear Stress " according to which is required. • Multiply the applied direct stress by this factor. This gives the required maximum stress. Example "** Suppose a material be subjected to a shear stress of 5 ton /in.2 and to a direct stress of 10 tons/in.2. The ratio—shear stress/direct stress = 5/10 = 0.5, i.e. 0.5 tons/in.2 shear stress for each 1.0 ton/in.2 direct stress. Look up this value on the perpendicular. The arc which if drawn would intersect this point would have a factor of nearly 1.21 ,(or more accurately 1.207) on the max direct stress scale and nearly 0.71 or* the max. shear stress scale. Hence— Max. direct stress =1.21 x 10=12.1 tons/in. very approx, and Max. shear stress=o.7i x 10= 7.1 tons/in - very approx. Principle of Construction Any equation of the form / V | ^ can be solved graphically by drawing a right angled triangle having the sides adjacent to the right angle proportional to the square roots of quantities under the root sign. The hypotenuse will then give the solution when measured to the (Continued on p. 303)
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