. Practical structural design; a text and reference work for engineers, architects, builders, draftsmen and technical schools;. oment, 2 4 8 which took into consideration the weight of the beam. This gives L\ wU M = {R2X ^j g EXTERNAL FORCES 27 Third. — The moment due to the concentrated load mustbe subtracted. The load is multiplied by the distance from the middle of the beam to the load = f — - a j; this giving P x [ — ~ a ] = -^ + Pa, and as this is to be subtracted the minus PL PLsign is placed before —? thus, —- Fourth. — The whole expression now appears, ,, „ L „ PL wL^M = R2X^ + Pa--^ g
. Practical structural design; a text and reference work for engineers, architects, builders, draftsmen and technical schools;. oment, 2 4 8 which took into consideration the weight of the beam. This gives L\ wU M = {R2X ^j g EXTERNAL FORCES 27 Third. — The moment due to the concentrated load mustbe subtracted. The load is multiplied by the distance from the middle of the beam to the load = f — - a j; this giving P x [ — ~ a ] = -^ + Pa, and as this is to be subtracted the minus PL PLsign is placed before —? thus, —- Fourth. — The whole expression now appears, ,, „ L „ PL wL^M = R2X^ + Pa--^ g— When adding positive and negative quantities add each kindseparately. difference of the sums and prefix the signof the greater sum. By inclosing the two negative quantities ina parenthesis the sign of the second is changed, so the full expressionmay be written 8 The arithmetical work is simple, as here shown q V 225\Af = (300 X 5 + x ) - (300 x + J = 1753 ft. lbs. Graphical Methods To divide a line into any number of equal parts use the geo-metrical principle of similar 6 7 6^ Fig. 20 — Division of Line into Equal Parts In Fig. 20 let AC represent a hne that is to be divided into anynumber of equal parts. The length is such that no regular scalecan be used readily for the purpose. Set off from one end a line,AB, Sit any angle. This line is drawn to some scale and dividedinto as many equal parts as it is desired to divide the line B to C and through the divisions on the line AB drawlines parallel to BC, as shown. 28 PRACTICAL STRUCTURAL DESIGN A number of curves are used by engineers and scientists, themost useful of which, and the only one used by structural de-signers, is the parabola. This curve is formed by cutting a section
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