Columns a Treatise On the Strength And Design of Compression Members

Cover Columns a Treatise On the Strength And Design of Compression Members
Columns a Treatise On the Strength And Design of Compression Members
E H Ernest Hinkly Salmon
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THE NON-HOMOGENEOUS BRACED COLUMN (FIDLER'S ASSUMPTIONS) The cross section (Fig. 10) consists of two flanges connected together by a stiff web. The effect of secondary flexure in the flanges is supposed to be negligible. The cross section is uniform, and the column originally straight. The load is applied at the centres of area of the end cross sections, and in the direction of the unstrained central axis. The modulus of elasticity is different in each flange, L but uniform throughout their len...gth.
Let EI be . The value of the modulus in the 1 convex flange, and E 3 that in the concave flange. . As in Variation 4, the curvature will be uniplanar, __ 4 Jv an( ^ *k e axes CCoC and DDoD perpendicular to the 2 ~*] plane of bending. The centre of resistance Dp will k- Uj-*t*- u 2 -i f a ii on tne convex s jd e o f CCoC, and EI will be FIG. 10. Greater than E 2 .
Let a\ be the area of the convex flange and a 2 that of the concave. Then a = a : + a 2 .
From equation (2) dW whence Therefore, w w (66) EI#I -f- E 2 a 2 E a a where E a a E\a\ -f- E 2 a 2 .


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