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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 3.83 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 3.144 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 3.144 indicates that the sum of all distribution factors at a joint should equal 1.0. 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. 3.135a and b with Oa 0. . Moments distributed to fixed supports remain at the support i.e. 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 1.0. To illustrate the method member end moments will be calculated for the continuous beam shown in Fig. 3.75a. All joints are initially locked. The concentrated load on span AB induces fixed-end moments of 9.60 and -14.40 ft-kips at A and B respectively see Art. 3.37 . The uniform load on BC induces fixed-end moments of 18.75 and -18.75 ft-kips at B and C respectively. The moment at C from the cantilever CD is 12.50 ft-kips. These values are shown in Fig. 3.80a. The distribution factors at joints where two or more members are connected are then calculated from Eq. 3.144 . With EỉAB LAB 200E 120 1.67E and EỉBC LBC 600E 180 3.33E the distribution factors are DBA 1.67E 1.67E 3.33E 0 33 and DBC 3.33 5.00 0.67. With EỉCD LCD 0 for a cantilevered member DCB 10E 0 10E 1.00 and Dcd 0.00. Joints not at fixed supports are then unlocked one by one. In each case the unbalanced moments