Bolt Cross

Wheel bolt dimensions?

Hi,

I am trying to figure out the diameter of the wheel bolt in a car wheel, a car that breaks with locking it's wheels in these conditions:
- the mass of the car is 1500 kg
- all the weight of the car is shifted on the front wheels
- only the front wheels brake
- the friction coefficient between tire and road is 0.5
- a wheel has 5 bolts that are placed on a circle of 50 mm radius centered in the wheel center
- the total radius of the wheel+tire is 316 mm
- the car produces a torque of 285Nm at 1800 rpm
- the modulus of shearing (I'm not sure if the translation is correct, I'm not a native English speaker) is 100 MPa (the maximum effort that the steel can hold before breaking)

Thank you!

Kind of abusive on the car, maybe?

first lets find the force the road applies to the wheels
normal force is mg
so frictional force is 0.5mg
F = 0.5(1500)(9.81)
F = 7360 N

summing forces about the center of the locked up tire we can determine the force the wheel bolts create to resist the braking load. I'll assume the friction force between the wheel and hub is zero so that all force is carried by the bolts.

7360(316) - Fb(50) = 0
Fb = 46500 N

Assume each bolt is equally loaded on two tires (10 bolts)
each bolt carries
46500/10 = 4650 N

so each bolt cross sectional area is found by dividing by the shear modulus (good job on the english)

A = 4650/100x10^6
A = 4.65x10^-5 m^2

as area for a circle is (pi)r^2
(pi)r^2 = 4.65x10^-5
r = 0.00385 m
so round up to
r = 4 mm
d = 8 mm

This is a minimum and has no factor of safety.

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