Final

Name Surname:

Student iD

$2022-2023$ Fall Semester $-$Duration: $100$ minutes

Course Nathe : cvin $222-$ Mechanics of Mroup: $.....$

Date!

$(3095)$ A WT$20530$ structural steel section is used for a $6\mathrm{.}5-m$ column. Assum

pinned connections at each end of the column. Determine:

$($a$)$ the slenderness ratio.

$($b$)$ the Euler buckling load $($Par$).$ Use $E=200$GPa for the steel.

$($c$)$ the axial stress in the column when the Euler load is applied $({}_{cr}).$

The following section properties for a standard steel WT$20530$ shape are given as

$A=3,800m{m}^2,l_4-13\mathrm{.}8{10}^{6}m{m}^4,r_3-87\mathrm{.}7mm,l_y=5\mathrm{.}99{10}^{6}m{m}^4,r_y=39\mathrm{.}6mm$

$(40\%6)$ Consider a point in a structural member that is subjected to plane

stress. Normal and shear stresses acting on horizontal and vertical planes at

the point are shown in Figure.

$($a$)$ Determine the principal stresses and the maximum in$-$plane shear stress

acting at the point by using the Mohr's Circle.

$($b$)$ Show these stresses on an appropriate sketch.

$($c$)$ Compute the absolute maximum shear stress at the point.

$(15\%)$ A simply supported wood beam with a span of $L=5m$ supports a uniformly distributed

load of wo$.$ The beam width is $b=140mm$ and the beam height is $h=260mm.$ The allowable bending

stress of the wood is $9\mathrm{.}5$MPa.

Calculate the magnitude of the maximum bending moment and distributed load wo may be carried by

the beam.

$(15\%)$ Applying super$-$positioning methods, determine the vertical deflection and slope for the

beam shown in Figure at the midpoint $B.$ Assume that $EI$ is constant for the beam. $($Related table have

been attached to this question$)$