Question $(1)$

$(20$ Marks$)$

Choose the most correct answer for each of the following questions;

According to this course lectures, mid$-$span deflections due to bending moment for simply supported beams that are subjected to concentrated loads at the centre can be calculated using this formula $.$ If $L=4d,$ which beam $($A or B$)$ would experience greater mid$-$span deflection, if we consider the beam deformations occurred due to both shear and bending moment. Assume that both beams have the same $EI.$ G$.$ and cross$-$sectional area.

$($a$)$ Both beams would experience the same exact mid$-$span deflection.

$($b$)$ Beam $($A$)$ would experience slightly greater mid$-$span deflection.

$($c$)$ Beam $($B$)$ would experience slightly greater mid$-$span deflection.

$($d$)$ Cannot decide on which beam would experience greater mid$-$span deflection without knowing the magnitude of the applied load $($P$).$

Which of the followings can be modeled using plane$-$stress finite elements, such as CST or Q$4$ elements?

$($a$)$ A concrete floor slab in a building with vertical loading applied to it$.$

$($b$)$ A wall carrying vertical loading in its plane and is subjected to transverse wind loading concurrently.

$($c$)$ A thin steel plate that is subjected to tensile stresses.

$($d$)$ All the above.

Which of the followings is valid in plane$-$stress analysis?

$($a$)$ Stresses and strains are always constant in the plane of the problem.

$($b$)$ Only stresses are always constant in the plane of the problem.

$($c$)$ Only strains are always constant in the plane of the problem.

$($d$)$ Non of the above.

Finite element computer modelling is a very powerful tool to solve sophisticated problems. However, the reliability and accuracy of the computer FE model is highly dependant on;

$($a$)$ The shape of the finite elements used in the computer model.

$($b$)$ The size of the finite elements used in the computer model.

$($c$)$ The aspect ratio $($width$/$height$)$ of the finite elements used in the computer model.

$($d$)$ All the above.