tailieunhanh - Structural Steel Designers Handbook Part 3

Tham khảo tài liệu 'structural steel designers handbook part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | GENERAL STRUCTURAL THEORY In general if all joints are locked and then one is released the amount of unbalanced moment distributed to member i connected to the unlocked joint is determined by the distribution factor Di the ratio of the moment distributed to i to the unbalanced moment. For a prismatic member Eỉ L Di ii1 1 J Ejỉ L 1 1 where S 1 E1ỉj L1 is the sum of the stiffness of all n members including member i joined at the unlocked joint. Equation indicates that the sum of all distribution factors at a joint should equal . Members cantilevered from a joint contribute no stiffness and therefore have a distribution factor of zero. The amount of moment distributed from an unlocked end of a prismatic member to a locked end is 1 2. This carry-over factor can be derived from Eqs. and b with Oa 0. . Moments distributed to fixed supports remain at the support . fixed supports are never unlocked. At a pinned joint non-moment-resisting support all the unbalanced moment should be distributed to the pinned end on unlocking the joint. In this case the distribution factor is . To illustrate the method member end moments will be calculated for the continuous beam shown in Fig. . All joints are initially locked. The concentrated load on span AB induces fixed-end moments of and ft-kips at A and B respectively see Art. . The uniform load on BC induces fixed-end moments of and ft-kips at B and C respectively. The moment at C from the cantilever CD is ft-kips. These values are shown in Fig. . The distribution factors at joints where two or more members are connected are then calculated from Eq. . With EỉAB LAB 200E 120 and EỉBC LBC 600E 180 the distribution factors are DBA 0 33 and DBC . With EỉCD LCD 0 for a cantilevered member DCB 10E 0 10E and Dcd . Joints not at fixed supports are then unlocked one by one. In each case the unbalanced moments