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Aviation History
1913
1913 - 1123.PDF
OCTOBER 18, 1913. If Mi, M2, M3 are the bending moments at three consecutive supports ABC of a continuous beam, (6AJX, 6Anjc2 HID M, 1, + 2M, (i, + 1.) + M, — + - • - - - - j, ,a where A] = area of BM diagram for portion AB if separate and simply supported. Aj = do for portion BC. Xi = distance of CG of area Ai from support A measured along beam. x« = distance of CG of area A2 from support C measured along beam. I, = span AB. i2 = span BC. Applying this in the case of the three supports ABC of the spar we have 7-5 x 116 + 2MS(7'S + 5-48) + S-48M3 = 3578 i.e. 25-96^2 + S"48M3 = 3548- 870 = 2708. Again applying the same theorem in the case of the 3 supports, BC C, we have 5-48 M2 + 2M3 (5-48 + 1-84) + 1-84 M3 = 965 i.e. 5-48 M2 + 16'48 M3 = 965. We now have two equations in M2 and M3 and these determine the value of M2 and M8 • M2 = 98 lbs. ft. M3 = 25 lbs. ft. (k) The bending moment at the supports are marked off on the diagram and the points for consecutive supports joined by straight lines. On these lines the original total bending moment diagrams are erected, making vertical distances from the line equal to vertical distances of the original from the axis. The result is the bending moment diagram for the continuous spar as shown in Fig. 5. (4) Loads in Struts and Wires and End Loads In Spars.—Determine the resultant vertical forces at the supports of the spars allowing for bending moment. Example (1). Resultant vertical force at The deflection is found by integration of the slops diagram, which. is first obtained by integration of the bending moment diagram. If P = end load at any section (compression), d = deflection, M = bending moment, z = modulus of bending, A — area of section, Then stress at outer fibre M + 2Vd _P s A' (6) The margin of strength of struts should be based on their crippling loads. From tests made at the R.A.F., the following formula is found to give approximate values for the crippling loads of spruce and ash pin-jointed struts :— Crippling load in lbs. = 1 A Flfi-6 Where F = 5,600 lbs. per sq. in. for spruce, = 6,250 ,, ash, A = area of section, L = length, k =. least radius of gyration of section, a = constant which depends on value of as shown iiv Fig. 6. * (7) Stresses Due to Drift.— The maximum load on the pla n COMPARISON OF STRENGTHS OF ASH AND SPRUCE STRUTS support A=i7-i5 (3-55 + 375) + + 2-4 = M, = 125-1 Resultant vertical force at support B = I7-I5(3'75 + 2-74) • M,-M2 7-5 127*5 lbs- •M, MrMj 7-5 5H8 = III"2 - 2"4+ 13-3 = I22'I lbs. The resultant vertical forces for the bottom spar * having been similarly found, the loads in the struts, wires and spars can be found as in section (3) (/). For strict accuracy the bending moment diagram should be recalculated using the new loads found for the wires, but this is unnecessary for practical purposes. (5) Stresses in Spars.-—To estimate the stresses in the spars, the stress due to bending moment is added to that due to end load. For sections not very neat the supports, and where the end load is compressive, the extra bending moment due to end load and deflection must be added to the bending moment due to the lift. If P is the end load and d is the deflection at the section, the amount 2 Pd should be added to the bending moment, the product Vd being doubled to allow for extra deflection due to end load. ® ® due to drift can be taken as a uniformly distributed horizontal loaa of one-sixth of the lift, equally divided between the spars. If the drift is taken by the internal drift wires the rear spars are put in compression and the front spars in tension. If taken by the external wires the front spars are put in compression. The loads in the spars and wires are calculated in the same way as for an ordinary braced structure, and should be added to those due to lift. ^ , »«•;•, A Breguet getting ready to ris;. 1149
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