Essentials in the theory of framed structures . 283 Hence the strain or change in length of a member may bedetermined if its length and cross-sectional area, the stresswhich it resists and the modulus of elasticity of its materialare known. Experiments show that, for any given material,the modulus of elasticity is approximately constant for allunit stresses below a certain limit, called the elastic elastic limit for structural steel is about 60 per cent of itsultimate strength; hence the permissible unit stress in allcurrent practice is well within the elastic limit. The modulusof el
Essentials in the theory of framed structures . 283 Hence the strain or change in length of a member may bedetermined if its length and cross-sectional area, the stresswhich it resists and the modulus of elasticity of its materialare known. Experiments show that, for any given material,the modulus of elasticity is approximately constant for allunit stresses below a certain limit, called the elastic elastic limit for structural steel is about 60 per cent of itsultimate strength; hence the permissible unit stress in allcurrent practice is well within the elastic limit. The modulusof elasticity for ordinary structural steel is about 29,000,000lb. per square inch; hence if a member 50 ft. long, having across-sectional area of 20 sq. in., is subjected to a tensile stressof 300,000 lb., the strain or elongation of the member will be „ 300,000 X 50 X 12 D = ^ = m. 20 X 29,000,000 Sec. I. Algebraic Method 179. The algebraic solution may be developed by equatingthe external work done by the external forces, to the internal. work performed upon the members of the truss. Let Ai (Fig. 17s) represent the vertical component of the dis-placement, or deflection of the points in the direction of the forceFi. During the movement of the point from B to B, the forcewhich has been increased from zero to Fi performs work to theamount of K -PiAi- Each member under stress, and therebysubject to strain, contributes its share to the deflection of any member HK, for example, which is I inches longand has a cross-sectional area of A sq. in. Let Pi, P2 and Pz 284 THEORY OF FRAMED STRUCTURES Chap. VII represent the stresses in HK, caused by the loads Fi, F^ and F3 respectively; and let Pi + P2 + -Ps = -P = the total stress. PIThe strain in HK is D = -r-p; AE and the total work performed upon HK, as the three loads are applied and the stresses gradually increased from zero to their final values, is -(Pi + P2 + P,)D = -PD =- P^2 22 AE The work performed upon HK, resulti
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
