Part $2$: Calculation of machine elements $(90$ points$)$

Introduction to the calculation questions:

Calculation of the ramp

When the trailer is loaded with a mobile machine, it's weight per wheel $mw$ causes a wheel load $F_w$ in vertical direction $($see figure$).$ This load results in a normal load $F_N$ and a friction force FR in between the wheel and the ramp. Determine the stresses in the girders of the ramp for the below given load condition.

Assumption: friction in between the ground and the ramp can be ignored! Note: the given bending resistance $W_B$ belongs to the entire profile consisting of both girders

Add all results to the given table!

Mobile machine weight per wheel:

Load application factor:

Ramp angle

Ramp length

Profile height

Profile width:

Profile thickness:

Bending resistance for the profile:

Minimum safety factor:

Material of the ramp:

Student No$.$: $q,$ a$)$ Determine the maximum loads $F_N$ and $F_R$ for the ramp to be analyzed if the wheel is exactly in the middle of the ramp $($see sketch$).$ c$)$ Calculate the stresses for the given cross section, select a stress hypothesis and determine an equivalent stress oeq. d$)$ Define a reference dimension for the cross section and determine the permitted stress under consideration of the technological size factor for the profile and the given safety factor. Plastic deformation has to be avoided!

e$)$ Compare the calculated equivalent stress to the permitted stress and determine the resulting safety factor $S_{0,\text{r}\text{e}\text{s}}$ for the profile.

$m_W=3000kg$

$K_A=1\mathrm{.}2$

$a=11\mathrm{.}5$

$l=2500mm$

$h=120mm$

$b=60mm$

$t=12mm$

$W_B=2*\frac{b*h^3-(b-t)*(h-2t{)}^3}{6*h}$

$S_{\text{D}\text{i}\text{n}\text{i}\text{n}}=1\mathrm{.}2$

mild steel, $S355$

$R_{eN}=355\frac{N}{m}{m}^2$

$R_{mN}=540\frac{N}{m}{m}^2$

Pagn $8$ of $22$ Page$($s$)$