Statically indeterminate stresses in stiff framed structures . ll be considered as stated,thus making the equations simpler for use in calculation. The following conventions will be followed throughout thework, and must be observed in applying all formulas: 1. The change in slope is positive when the tangent tothe elastic curve is turned in a clockwise direction. 3. Distances and deflections are positive when they aremeasured in the same direction from the base line asare positive slopes. sum of the 5. The bending moment is positive when theAmoments of allforces to the left of a section in a b
Statically indeterminate stresses in stiff framed structures . ll be considered as stated,thus making the equations simpler for use in calculation. The following conventions will be followed throughout thework, and must be observed in applying all formulas: 1. The change in slope is positive when the tangent tothe elastic curve is turned in a clockwise direction. 3. Distances and deflections are positive when they aremeasured in the same direction from the base line asare positive slopes. sum of the 5. The bending moment is positive when theAmoments of allforces to the left of a section in a beam is will be plotted on the tension,or convex, sideof the member. 4. The deflection D is measured from base line to theelastic curve of ^he member. 5. The distance QL s measured from base line to thetangent to the iastic curv, 6. The tangential deviation y is measured from the tan-gent to the elastic curve, to the elastic curve. All deflections are measured normal to the bsse line,which is the unstrained position of the elastic curve. 8. DERIVATION OF FUND/MENTAL EQUATIONS. Case 1. Member in flexure carrying no external load. In Fig. 13, AB representsthe unstrained position of theelastic curve of a member, andAB represents the strainedposition of the elastic curveof the same member. The changesin the slopes of the tangentsto the elastic -mrve at A andB are GA and © total movement of A normal/*> AB is D. The m/EI diagramis shown by Fig. 14, in which E and I are considered constant. Nowconsider the quantities shown at the point B. The deflection D iscomposed of two quantities; the tangential deviation y^t and thedisplacement due to the change in slope at A, or Before ex- pressing these quantities in terms of the bending moments, it iswell to note that the algebraic sum of the areas of the M/EI dia-gram is equal to the algebraic sum of the areas abe and ede. Hencethe position of the point q need not be located. The tangentialdevia
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Keywords: ., bookcentury1900, bookdecade1910, booksubjecttheses, bookyear1915
