Statically indeterminate stresses in stiff framed structures . diagram. Hence q q L |m/ + E ] (*). Multiplying equation (a) by 3, and equation (b) by L, and combin-ing, gives 3D - 30AL . g ©t>1» - ©AL * f£ B A El 1 £ t 4 8 2 29AL + 9BL - 3D s - f or EI 2 Similarly, 2EI ZQA f 9B - 3D/L • • • • • L2 3D - 36 a L s „A IT *A + % 26BL - 20AL - ±- 20BL t 9aL - 3D = L2. MB , or IT 2~ 2Ej:L 20B + 0A - 3D/l These equations are made more convenient for use by substitutingK r i/L, and R r D/L, whence MA = -2EK (20A 0B - 3R, MB z 2EK (20B t 9A - 3R) , (1). 17. Case 2. Member in flexure parrying £ concen
Statically indeterminate stresses in stiff framed structures . diagram. Hence q q L |m/ + E ] (*). Multiplying equation (a) by 3, and equation (b) by L, and combin-ing, gives 3D - 30AL . g ©t>1» - ©AL * f£ B A El 1 £ t 4 8 2 29AL + 9BL - 3D s - f or EI 2 Similarly, 2EI ZQA f 9B - 3D/L • • • • • L2 3D - 36 a L s „A IT *A + % 26BL - 20AL - ±- 20BL t 9aL - 3D = L2. MB , or IT 2~ 2Ej:L 20B + 0A - 3D/l These equations are made more convenient for use by substitutingK r i/L, and R r D/L, whence MA = -2EK (20A 0B - 3R, MB z 2EK (20B t 9A - 3R) , (1). 17. Case 2. Member in flexure parrying £ concentrated exter-nal load P at a distance a from the end B. Fig. 15 represents a member similar to the one shownin Fig. 13, except that a con-centrated load P is applied ata distance a from B. The M/EIdiagram shown in issimilar to the m/EI diagram forthe member shown in Fig. 14,withthe M/EI diagram for a simplebeam carrying the load P, super-imposed upon it. Now considerthe deflection at the point B. The tangential deviation is equalto. D - 0AI which reduces to m I MBL + MAL Pab (i * EI [ 6 3 J + EEIL [ (Is , *Ja f b fa f b\3 \ 3/ D - 0AL * MBL Pab . , (c). The change in slope from B to A is expressed by ©B - 9^, A EI MB Ma £sib r + f- t jr Combining equations (c) and (d) to eliminate MB, gives 2©AL + ©BL 3D s EI /-MAL - Pa2b 2L , or 2EI 2©A + 9B- 3L/lj Pa2b - %T ? • • 18. Similarly, combining equations (c) and (d) to eliminate M .gives 20BL + ©AL - 3D EI —+-T~\ 2 _ L IT 2n whence Eeb2 L2 Substituting Kr i/l, and R» D/L, the equations for and M-g MA = -2EK ( 2©A + 9B T-3R) - Pa2b/L2 ^M-g s 2EK ( 2©fi + ©A -*r 3R) - Pab2/L2 J become (2). Case 3. Member in flexure carrying a series of loadssymmetrical sbout the middle of the member. Fig. 17 shows a mem-ber carrying a series of loadswhich is symmetrical about themiddle of the member. The M/EIdiagram for this member issimilar to that of ,withthe M/EI diagram of a simplebeam carry
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