Question

Section A: Answer all the questions. (Each question carries 5 marks). Q.1. Explain in your own words the requirements an indeterminate structure should satisfy and name the methods used to analyse indeterminate structures. Q.2. Explain in your own words the formation of plastic hinge in beams and draw stress distribution diagram at the section where plastic hinge is formed.

Answer 1

1) Statically indeterminate structures occur more frequently in practice than those that are statically determinate and are generally more economical in that they are stiffer and stronger. For example, a fixed beam carrying a concentrated load at mid-span has a central displacement that is one-quarter of that of a simply supported beam of the same span and carrying the same load, while the maximum bending moment is reduced by half. It follows that a smaller beam section would be required in the fixed beam case, resulting in savings in material.and also in indeterminate structures we can can use post buckling strength of structure is stucture is made of steel, as in steel structure failure occurs by formation of plastic hinges.

The following methods are used to solve indeterminate stucture

1)slope deflection method

2)moment distribution metho3) strain energy method

Question 2), A plastic hinge in structural engineering, refers to the deformation of a part of a beam wherever plastic bending happens. Hinge means that having no capability to resist moment. Therefore, a plastic hinge behaves like a standard hinge - permitting free rotation. The concept of plastic hinge is important in understanding structural failure.Plastic hinges widen on small lengths of beams. The real values of this lengths depend upon load distributions and cross sections of beams. Elaborated analyses have shown that it is more than correct to think this beams rigid-plastic, with plastic deformation confined to plastic hinges at points. Whereas this assumption is decent for limit state analysis, finite part formulations are offered to account for the unfold of physical property on plastic hinge lengths.

Stress concentratation is shown by dark black in beam at the location of plastic hinge

partially plastic zone → W Scanged-with-eamscanner