In this thesis, free vibration of beam structures with initial load is analyzed. It is based on the theory of elasticity and the formulation is derived by finite element method. The present method is different from traditions beam theories and is able to simulate beam vibration more precisely. The free vibration frequencies of beams under initial axial loading and different boundary conditions and geometrical aspect ratios are solved first and compared with those of Timoshenko beam theory. Vibration of beams with initial lateral loading is then analyzed, considering only the initial stresses and both the initial stresses and the initial displacements induced by the initial loading, to reveal the effect of initial stresses and initial displacement on vibration of beams with initial loading.

This thesis studies the present methods used to predict the ultimate tripping strength of stiffened panels under compressive axial stress. The current methods involve the use of a bifurcation, or eigenvalue, approach to predicting failure stress. The effects of initial transverse eccentricity of the stiffener are ignored using such a method. Six panels were modeled and tested with ABAQUS, a finite element software package, and the results were compared to output from ULSAP, a closed-form ultimate strength analysis program. The ultimate strengths predicted by ABAQUS changed with the influence of initial deflection of the stiffener flange, while the results from ULSAP did not change. This thesis attempts to use beam-column analysis on the imperfect stiffener flange to predict the tripping strength. It was determined that the procedure presented in this thesis does not accurately model the true failure mode of stiffeners in tripping. The resulting ultimate strengths are extremely conservative and neglect the importance of the stiffener web's role in tripping. Future work is recommended to expand on these findings and to incorporate the influence of the stiffener web into a beam-column solution. / Master of Science

Structural design of piles with respect to buckling in Sweden is commonlymade in accordance with the calculation model from the Commission ofPile Research, PKR. A prerequisite for this model is that the elasticbuckling length of the pile is shorter than the physical length. For shortpiles this assumption might not be valid, meaning that anotherappropriate calculation model may be used instead. This situation occurswhen designing end-bearing piles in typical geological conditions foreastern Sweden, consisting of soft clay and shallow bedrock.This thesis compared the PKR-model with alternative models for thedesign of short piles. One of the alternate calculation models was a finiteelement model where Winkler springs represented the soil. It was used tosimulate cases with various diameters and undrained shear strengths.Furthermore, the results using the PKR- and FEM-model was comparedto calculations according to Eurocode 3 considering the pile as a freestandingcolumn. By the help of the FEM-model, a method to considergreater initial deflections in the Eurocode 3-model was also developed.In conclusion, the PKR-model was non-conservative for some of thetested cases. With some precautions taken for those cases, the model wasvalid to use for elastic buckling lengths up to two times the physicallength of the pile. The results from the Eurocode 3-model were bothconservative and non-conservative depending on the pile- and soilconditions. It was seen that the analytical models were not comparablesince they handle prerequisites and design assumptions in different ways.A sensitivity analysis was also made which resulted in suggestions forfurther research on the topic.