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# Advanced Structural Analysis and Design

The resultant ratio of the carry over moment of the transferred end to the fixed moment from the initial end is referred to as the carry over factor i. e. the moment which is transferred to the fixed end. This factor is dependent on fixity (F) of the joint that is opposite to the joint in question. Note F is equal to zero for pin joints and F=1 for built in joints. Distribution factors - The amount of moment that goes to any member is a function of stiffness, and any joints that are tributary to that joint.

The distribution factor is thus denoted as D= K/ ΣK where K is the stiffness factor for the joint in question and ΣK is the sum of stiffness factors of the joints tributary to this joint in consideration (Demetrios & Jim, 2007, 236). Question three. Slope-deflection and equilibrium equations Slope deflection is applied in beams, structures and frames which have curved members. This method applies a set of linear simultaneous equations which makes it complicated and time consuming. The method deploys two requirements i. e. compatibility and equilibrium. Compatibility is applied in the sense that the joints in a structure are assumed to be rigid i. e.

the angles between member joints do not change when loads are applied. All members on a joint are assigned one single angle of rotation. Equilibrium aspects are achieved through determining that the end moments of a member in a particular structure are related to its end replacements and end rotations (Nainan, 2005, 581). Equilibrium equations The following equilibrium equations are applied when determining the slope deflection parameters: for two different types of slopes, the equilibrium equations are rewritten as shown below where the angles of rotation are applied: Stability checks on a retaining structure: A retaining wall design is a structure that is meant to keep the level difference of the soil on its either side.

A number of forces have been determined to act on the structure.

These are weight of the structure, pressure of the retained soil, pressure of the foundation and pressure on the soil which is against the front wall, just to mention but a few. It is therefore important to check the stability of this wall as it’s affected by external forces. Calculations are used to determine the stability of the structure as if it were a single body. Two forms are taken i. e. the horizontal and the toppling of the wall. The first method is called the sliding stability, which assesses the horizontal forces and dividing into driving and resistance forces.

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