By Senator h. c, Dr. h. c., Dr. sc. techn. Dipl. Bau-Ing. Curt F. Kollbrunner ETH, SIA, Dr. Ing. (Ph.D.) Dipl. Bau-Ing. Konrad Basler ETH, SIA, M. ASCE (auth.)
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Extra info for Torsion in Structures: An Engineering Approach
This equation may be written for each cell as follows: (i = 1, 2, ... , n). 16) T represents the torsional moment acting on the whole cross section, Ai the area enclosed by the periphery of any cell i and the left side of this equation is the contour integral of the shear stress along this line. 3 Multicellular Box Section Members the slope of the membrane in the membrane analogy which is equal to the difference in lid elevation divided by the wall thickness, 7: = q/t. If the path of integration is further divided into parts which either separate two cells or coincide with the periphery, then the contour integral may be written as a sum of the corresponding integrals.
80i (f:r , _ tOi 8, 8 0; + 8i tOi ti t:' '0 8· = Fig. 17. Equivalent Wall Thickness t* for Branched Parts of the Wall. 35) makes it possible to compute the torsion constant as if one dealt with a simple monocellular cross section. 36a) According to Eqs. 33) it is divided into two parts which, with the notation of Fig. 36), has a smaller influence on the computation of the torsion constant and the shear flow qo than it has on the branch flows q; and qo;' A correction may readily be evaluated. The rotation of cell i together with the entire cross section causes a correction shear flow qi which is restricted to the walls enclosing cell i.
28) become: A = Ao + nA 1 1101, 1111 11~1 B='/')oo-n-, 1111 Fig. 15. n Equivalent Cells Added to One Common Base Cell. These expressions are now simple enough to permit replacement of A, B and C in Eqs. 32), whence K = 4 A~l111 + 2nAoA 11101 + nA~1100 1}oo'YJu - n1}io _ '!.... 34) nA~11oo' T Ao(1111 - 1101) - Al (1100 - n1101) . 2 A~1111 + 2nAoAl1101 + nA~1100 ~ The coefficients '/')00' '/')O}' '/')11' Ao and A} may be read from Fig. 13 in which i and k are thought to be replaced by 1. 34) have to become identical to those given for a bicellular cross section, Eqs.
Torsion in Structures: An Engineering Approach by Senator h. c, Dr. h. c., Dr. sc. techn. Dipl. Bau-Ing. Curt F. Kollbrunner ETH, SIA, Dr. Ing. (Ph.D.) Dipl. Bau-Ing. Konrad Basler ETH, SIA, M. ASCE (auth.)