Roof Design

CASE STUDY :

Bow–Roof Prediction Formula

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

Where,

L = Roof Length in X-Direction[mm](Roof dimension in 0-Y)

R = Roof curvature

R = 2(Rx*Ry)/(Rx+Ry)

Rx = X curvature

Ry = Y curvature

t = Roof plate thickness [mm]

l = Bow Roof Span [mm]

Judgment Condition

OK< 2.7

Here, value of L and t is common and L = 2024.4592 mm

t = 0.75 mm

- First Section ( Between front roof rail and bow roof 1 ) : Rx = 5739.3524 mm

Ry = 2532.5419 mm

R = 2(Rx*Ry)/(Rx+Ry)

= 2 (5739.3524*2532.5419)/ (5739.3524+2532.5419)

= 3514.34627 mm

I = 358.8260 mm

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

= [ 1.73 x 10^(-3) x 2024.4592] + [1.85 x 10^(-8) x (3514.34627)^2 / 0.75] + [ 1.10 x 10^(-3) x 358.8260] - 2.68

= 1.52167

Hence, OK = 1.52167 < 2.67 ( Hence it passes )

- Second Section ( Between bow roof 1 and centre roof ) : Rx = 4934.1917 mm

Ry = 6350.7075 mm

R = 2(Rx*Ry)/(Rx+Ry)

= 2 (4934.1917*6350.7075)/ (4934.1917+6350.7075)

= 5553.5468 mm

I = 491.3265 mm

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

= [1.73 x 10^(-3) x 2024.4592] + [ 1.85 x 10^(-8) x (5553.5468^2)/ 0.75] + [ 1.10 x 10^(-3) x 491.3265] - 2.68

= 2.12354

Hence, OK = 2.12354 < 2.67 ( Hence it passes )

- Third Section ( Between centre roof and bow roof 2 ) : Rx = 3865.4871 mm

Ry = 11160.2060 mm

R = 2(Rx*Ry)/(Rx+Ry)

= 2 (3865.4871*11160.2060)/ (3865.4871+11160.2060)

= 5742.115460 mm

I = 471.2272 mm

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

= [1.73 x 10^(-3) x 2024.4592] + [1.85 x 10^(-8) x (5742.115460^2)/0.75] + [ 1.10x10^(-3) x 471.2272] - 2.68

= 2.154

Hence, OK = 2.154 < 2.67 ( Hence it passes )

- Fourth Section ( Between bow roof 2 and Rear roof rail ) : Rx = 3238.1829 mm

Ry = 14866.8509 mm

R = 2(Rx*Ry)/(Rx+Ry)

= 2 (3238.1829*14866.8509)/ (3238.1829+14866.8509)

= 5318.0328624 mm

I = 261.5264 mm

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

= [1.73 x 10^(-3) x 2024.4592] + [1.85 x 10^(-8) x (5318.0328624^2)/0.75] + [ 1.10x10^(-3) x 261.5264] - 2.68

= 1.807603

Hence, OK = 1.807603 < 2.67 ( Hence it passes )

CASE STUDY :

Snow Load Prediction Formula

Qr = [Iy x t²] / [α x s x [(Rx + Ry)/2]² x 10^-8]

Note: The Qr value given over here is correct. There was a typo error in the formula given in the video.

Where,

α = My x Lx² x 10^-12 , My = Y(Ly-Y)

t = Roof plate thickness [mm]

Ly = Distance between the front and rear roof Rails on the Vehicle along with 0Y[mm]

Length of Roof panel with the center point between Roof rail Front /Rear as the front and rear reference point.

Lx = Distance between the Left and Right end of the roof on the Roof BOW [mm]

The width of the roof panel is exposed on the surface.

Y = Distance front Front Roof Rail to Roof BOW[mm]

s = Distance for which Roof BOW bears divided load [mm]

s = L1/2 + L2/2

Iy = Geometrical moment of inertia of Roof BOW (Y cross-section )[mm4]

Rx = Lateral direction curvature radius of roof panel Y cross-section on Roof BOW [mm]

Roof panel curvature Radius of the Length Lx in Front view

Ry = Longitudinal Direction curvature radius of the Roof panel X cross-section on Roof BOW [mm]

Roof panel X curvature radius of length s in Side view

Judgment condition

Qr ≥ 3.1

250 ≤ s ≤ 380

- First Section ( Between front roof rail and bow roof 1 ) : Rx = 4583.9522 mm

Ry = 2525.8059 mm

t = 0.75 mm

Iy = 2.49968 x 10^3 mm^4

L1 = 439.95 mm

L2 = 571.2321 mm

s = (L1 + L2)/ 2 = 505.591 mm

Ly = 1951.4 mm

Lx = 1120.9498 mm

Y = 439.95 mm

My = Y(Ly-Y) = 439.95 x ( 1951.4-439.95)

= 664962.428 mm^2

α = My x Lx² x 10^-12

= 664962.428 x (1120.9498)^2 x 10^(-12)

= 0.83554 mm^2

Qr = [Iy x t²] / [α x s x [(Rx + Ry)/2]² x 10^-8]

α = My x Lx² x 10^-12 , My = Y(Ly-Y)

Qr = [2.49968 x 10^3 x 0.75^2] / [ 0.83554 x 505.591 x [(4583.9522 + 2525.8059 )/2]^2 x 10^(-8)]

= 1406.07/ 53.3846 = 26.3385

Hence, Qr = 26.3385 > or = 3.1 ( Hence it passes )

- Second Section ( Between centre roof and bow roof 1 ) : Rx = 3767.7752 mm

Ry = 6178.5930 mm

t = 0.75 mm

Iy = 3.4462 x 10^3 mm^4

L1 = 571.2321 mm

L2 = 551.1486 mm

s = (L1 + L2)/ 2 = 561.19035 mm

Ly = 1951.4 mm

Lx = 1077.1 mm

Y = 1011.1872 mm

My = Y(Ly-Y) = 1011.1872 x ( 1951.4-1011.1872)

= 950731.149 mm^2

α = My x Lx² x 10^-12

= 950731.149 x (1077.1 )^2 x 10^(-12)

= 1.102985 mm^2

Qr = [Iy x t²] / [α x s x [(Rx + Ry)/2]² x 10^-8]

α = My x Lx² x 10^-12 , My = Y(Ly-Y)

Qr = [3.4462 x 10^3 x 0.75^2] / [1.102985 x 561.19035 x [(3767.7752 + 6178.5930)/2]^2 x 10^(-8)]

= 1938.4875/ 153.090723 = 12.6623447

Hence, Qr = 12.6623447 > or = 3.1 ( Hence it passes )

Report : Roof is that part of the vehicle which protects the passengers from all the external environmental features such as weather conditions and ensures safety of passengers. In this challenge, roof is designed successfully by following all the design parameters and created front roof rail, bow roof 1, central roof rail, bow roof 2 and rear roof rail by following the given master section and are all assembled in an assembly file.And finally it is thickened to a value of 0.75 mm to complete our roof design.

After the roof design, Draft analysis was performed on each part and it satisfied the industrial standards. And then we created special sketches to analyse and calculate Bow–Roof Prediction Formula value and Snow Load Prediction Formula value.These were calculated using the formula given and in the corresponding sections. And after detailed calculation it was concluded that the designed roof is satisfying and passing the Bow–Roof Prediction Formula value requirement and Snow Load Prediction Formula value requirement and hence the designed roof is of good and industrially satisfying quality.