EXACT SECANT STIFFNESS MATRIX OF TIMOSHENKO BEAM RESTING ON VARIABLE ONE-PARAMETER WINKLER FOUNDATION

摘要

For the first time, exact secant stiffness and loading matrices for Timoshenko beam resting on variable one-parameter Winkler foundation are developed, using the power series approach. Effect of shear on deflection is taken into account in constructing the uncoupled differential equations. The proposed exact element is analyzed thoroughly to include the effect of shear on both deflection and internal forces; the results of such rigorous analysis show that the proposed exact secant stiffness matrix gives a big saving in the computer time with better accuracy of results. The proposed problem solution is compared with finite element analysis performed using the multi-purposes package MSC/NASTRAN. The deflection due to shear is found to be considerable in beams having small span to depth ratios with large values of modulus of foundation. It is also concluded that effect of shear must be taken into account in settlement calculations.