Due: $28\mathrm{.}11\mathrm{.}2024$ Until $12$:$00$

QUESTION $-1$:

This question is from the coursebook. Replace all dimensions $($in inches$)$ with mm by multiplying each by a factor $25.$ Also replace all forces $($in lbf$)$ with N by multiplying each by a factor $4\mathrm{.}5.$

a$)$ Write the loading function using singularity functions.

b$)$ Obtain the shear force and bending moment functions in terms of singularity functions.

c$)$ Using the shear force and bending moment functions, obtain the reactions $($in terms of forces and dimensions$)$

d$)$ Using the MATLAB code derived in the lectures, modifying it to work with the above found shear force and bending moment functions, obtain the shear force$-$bending moment diagrams.

e$)$ Change at least three dimensions $($which will create six different loadcases$)$ and obtain the shear$-$force and bending moment diagrams for all these loadcases.

Note: You will have seven $(7)$ shear$-$force and bending moment diagrams each of them will be in two planes $(\backslash ($ x$-$y $\backslash )$ and $\backslash ($ x$-$z $\backslash )).$

f$)$ Modify the MATLAB code by adding necessary instructions to evaluate magnitude of the total moment along the shaft. Plot the magnitude of the total moment along the shaft for above stated seven load cases.

g$)$ Modify the MATLAB code by adding necessary instructions to evaluate the maximum magnitude of the normal stress due to the bending moment at every location. Also, obtain, with the code, magnitude of the shear stress at every point of the shaft. Using these values, and modifying the MATLAB code, evaluate the principal stresses at every location of the shaft for above stated seven loadcases.