Roof challenge

AIM: To design a roof with all its components i.e. the front roof rail, bow roofs, center roof rail and rear roof rail by following the master sections and check for draft analysis also do the section inertia and curvature study.

ROOF:

The roof or top is the portion of an automobile that sits above the passenger compartment and it protects the occupants from various environmental conditions like heat, snow, rain, and winds. There are many types of the roof which differs based on the variants of the car and the region. The roof must be designed in such a way that it would able to withstand load or impact due to accidents or objects falling on it and other environmental factors, other factors like headroom, aesthetics play a role in the design. The roof is an assembly of many parts like Front roof rail, Bow roofs, Centre roof rail, and Rear roof rail. The number of bow roofs is based on the length of the roof and sometimes even the bow roof center is avoided in cases like small cars. The roof is attached to the body of the car using mastic sealants provided between bow roofs and the front and rear rails. Roof is connected to A-pillar, B-Pillar and C-Pillar to cover the front and rear door.

The Components of Roof:

• Front Roof Rail
• Bow Roof 1
• Centre Roof Rail
• Bow Roof 2
• Rear Roof Rail

MASTER SECTIONS:

All the components and flanges are designed according to the master sections and follow the dimensions in it.

FRONT ROOF RAIL:

Roof Outer Panel

Front Roof Rail

Bow Roof 1

Centre Roof Rail

Bow Roof 2

Rear Roof Rail

ROOF ASSEMBLY

BOW-ROOF PREDICTION FORMULA:

W = [1.73 x 10^-3 x L] + [1.85 x 10^-8 x R²/t] + [ 1.10 x 10^-3 x l] - 2.68

Judgment Condition

OK< 2.7

Where,

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

R = Roof curvature

R = 2(R_x×R_y)/(Rx+Ry)

Rx = X curvature

Ry = Y curvature

t = Roof plate thickness [mm]

l = Bow Roof Span [mm]

S.No	BOW	Rx	Ry	R	l	L	t	R2/t	W	OK/NG
1	Front-1st Bow	2522.8162	5739.6016	3505.0175	389.6327	2033.7048	0.75	16.3801×106	1.5699	OK
2	1st Bow-Centre	6267.0081	4955.0142	5534.3169	421.4924	2033.7048	0.75	40.8382×106	2.0574	OK
3	Centre-2nd Bow	10552.3977	2431.0168	3951.6655	406.2750	2033.7048	0.75	20.8208×106	1.6703	OK
4	2nd Bow-Rear	14468.3036	2783.0713	4668.1868	347.3025	2033.7048	0.75	29.0559×106	1.7578	OK

SNOW LOAD PREDICTION FORMULA:

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

Judgment condition

Qr ≥ 3.1

250 ≤ s ≤ 380

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 from 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

S.NO	BOW	Iy	α	Lx	Ly	Y	s	Rx	Ry	t	Qr	Determination (Qr)
1	Front-1st Bow	234.3731	0.97	1137.4147	2033.7048	489.5	496	2612.7699	4522.0002	0.75	2.15	NG
2	1st Bow-Centre	245.7732	0.90	1086.4165	2033.7048	502.5	495.35	6169.9630	3767.3657	0.75	1.25	NG
3	Centre-2nd Bow	234.4053	0.84	1058.5443	2033.7048	488.2	487.35	11038.4044	16962.9274	0.75	0.16	NG
4	2nd Bow-Rear		0.82	1044.4469	2033.7048	486.5		16227.6217	13381.7292	0.75

SECTION INERTIA STUDY:

Section Modulus:

• Section Modulus is the geometric property of the given cross-section of any shaft or beam structures
• It is the direct measure of the strength of the shaft section or the beam section
• Higher the section modulus of a structure, the more the resistive it becomes to bending
• It is the ratio of total moment resisted by the section to the stress in the extreme fibre
• It gives us an idea about how much of load the given structure can take

Section Modulas can be calculated by the formula:

S = I/y

Where, S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

FRONT ROOF RAIL:

I_max = 1.6819×10⁴ mm⁴

I_min = 908.7656 mm⁴

y = 123.9760/2

= 61.988 mm

S = I/y

= 908.7656/61.988

S = 14.6603 mm³

BOW ROOF 1:

I_max = 3.7436×10³ mm⁴

I_min = 234.3731 mm⁴

y = 74.8960/2

= 37.448 mm

S = I/y

= 234.3731/37.448

S = 6.2586 mm³

CENTRE ROOF:

I_max = 4.9589×10³ mm⁴

I_min = 245.7732 mm⁴

y = 82.1810/2

= 41.0905 mm

S = I/y

= 245.7732/41.0905

S = 5.9812 mm³

BOW ROOF 2:

I_max = 3.6846×10³ mm⁴

I_min = 234.4053 mm⁴

y = 74.3038/2

= 37.1519 mm

S = I/y

= 234.4053/37.1519

S = 6.3093 mm³

REAR ROOF RAIL:

I_max = 6.2073×10⁴ mm⁴

I_min = 3.1989×10³ mm⁴

y = 201.9963/2

= 100.9981 mm

S = I/y

= 3.1989×10³/100.9981

S = 31.6728 mm³

DRAFT ANALYSIS:

Roof Outer Panel

Front Roof Rail

Bow Roof 1

Centre Roof Rail

Bow Roof 2

Rear Roof Rail