tailieunhanh - Fundamentals of Structural Analysis Episode 2 Part 6

Tham khảo tài liệu 'fundamentals of structural analysis episode 2 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Other Topics by S. T. Mau Prismatic members O E _ b Mab 6EKộ 2L Mba 6EKộ Non-prismatic members b Mab - Sab CbaSba ộ T Mba - Sba CabSab Ộ Moment-rotation formulas for non-prismatic members member rotation. Using the identity in Eq. 1 the moment rotation formulas can be recast as Mab -Sab 1 Cab ộab 2 Mba -Sba 1 Cba ộab 2 Combining the above formulas we can write the moment-rotation formulas for a non-prismatic member as Mab Sabỡa CbaSbaỡb -Sab 1 Cab ộab Mfb 3 Mba CabSabỡa Sbaỡ -Sba 1 Cba ộab Mfa 3 These two equations are to be used in any displacement method of analysis. A sample of the numerical values of the factors in these two equations is given in the table below for two configurations of rectangular sections. The EK in the table refers to the EK calculated from the least sectional dimension of the member. 275 Other Topics by S. T. Mau Stiffness and Carryover Factors and Fixed-End Moments I I 1 I Cab Cba Sab Sba 1 rn Pn 1 1 L 2 L 2 1 w MFab MFba MFab MFba b a h h I Cab Cba Sab Sba 1 rn Pn 1 1 L 2 L 2 1 w MFab MFba MFab MFba Example 1. Find all the member-end moments of the beam shown. L 10 m. a 10 kN m 1 100kN c llllllllllllllllllllllllllllllllllllllllllllllllllll b _ h rh h h 1 I Non-prismatic beam example. Solution. We choice to use the slope-deflection method. There is only one DOF the rotation at node b db. The equation of equilibrium is 2 Mb 0 Mba Mbc 0 The EK based on the minimum depth of the beam h is the same for both members. The fixed-end moments are obtained from the above table 276 Other Topics by S. T. Mau For member ab MFab wl -67 kN-m MFba wL2 119 kN-m For member bc Mbc PL -159 kN-m MFcb PL 159 kN-m The moment-rotation formulas are Mba CabSabda Sbadb M ba 119 Mbc Sbcdb CcbScbdc MFbc - 159 The equilibrium equation Mba Mbc 0 .