TCV $4223$ CAT TWO Solid and Structural mechanics II $-$September December $2024$ Attempt all questions

i$.$ A beam ABC of length $9$ m has one support on the left end and the other support at a distance of $6$ m from the left end. The beam carries a point load of $1$ kN at the right end and also carries a uniformly distributed load of $4k\frac{N}{m}$ over a length of $3$ m as shown in the figure below. Determine the slope and deflection at point C $.$ Take Young's Modulus of material E as $200$Gpa and second moment of area I as $5$X$105m{m}^4(10$ Marks$).$

ii$.$ For the state of plane stress shown in Figure shown below, construct Mohr's circle and determine the principal stresses, maximum shearing stress and corresponding normal stress. Check your answer by use of analytical method $(20$ Marks$)$