How to work out how much weight a series of pre-stressed concrete lintels will hold?

Question

I will have a series of lintels (2.3m long) spanning a gap of 1.9m. The weight on top will be a car so the weight will be distributed over four points of contact. What information and calculations do I need to perform to work out the weight that can be supported?

Answer 1

Assume that the tires on one side of the car are resting over the support of the lintel on that side and that the load on each wheel of tha car is P in kg. Let's assume that the maximum allowable compression load of the concrete lintel is 210 kg/cm^2 and that the reinforcement of the lintel is of a balanced design.

The total compression on the lower half of the lintel section would be:

C = (1/2) c x 10 x 5 = 210 x 10 x 5/2  =  5250 kg

The equivalent bending moment is:

M = C x (2/3) x 5 = (10/3) x 5250 = 17500 kg-cm = 175 kg-m

Assuming that the gage spacing of the wheels is 1.83 meters, the distance of the other row of wheels from the other support is:

x = 1.9 - 1.83 = 0.07 m

Note: The gage spacing is the distance between the right side wheel and the corresponding left side wheel which is normally measured at the rear wheels.

The reaction on the other support would be:

R = 1.83P/1.9 = 0.963P

And the maximum bending moment on a lintel would be:

M = R x 0.07 = 0.07 x 0.963P = 0.06742P

Hence:

0.06742P = 175

P = 2596 kg

So the equivalent weight of the car that can be carried by the lintel series based on bending is:

W = 2596 x 4 = 10384kg

However, the lintels are also subjected to longitudinal shear. Assume that the maximum allowable shear stress of the concrete is v = 4.22kg/cm^2. The maximum shear force on a lintel is:

V =  0.963 P  

The allowable shear force on the concrete is:

V = (2/3)v bd^2; where b is the width of the beam and d is the depth of the beam. Thus;

V = (2/3)x 4.22 x 10 x 10^2 = 2813 kg

Hence;

0.963P = 2813

P = 2921 kg

The maximum weight of a car that can be supported by the lintel series based on longitudinal shear therefore is;

W = 4 x 2921 = 11684 kg

However, the lintels  are also subjected to a cutting (vertical) shear of 0.963P. With an allowable shear stress of 4.22 kg/cm^2, the maximum cutting shear force would be;

V = 0.963P = 4.22 xbd = 4.22 x10 x 10 = 422kg

P = 438.213 kg

The maximum weight of the car that can be carried by the series of lintels would therefore be:

W = 4 x 438.213 = 1753 kg

The allowable weight of the car that can be supported is the least of the calculated  values of W.

The  values of the car weights obtained above are based on the assumed characteristics of the reinforce concrete. If actual values are available, then use them in lieu of the assumed values.

Answer 2

what is supporting the lintels , brickwork or block .

Answer 3

for a car being carried upon a lintel:

1)the load of the car will b equally shared up by the 4 tyres of it= w/4

2)these point loads will b acting at their moment of inertia at the lintels hanging pt.

thus calculating their (total load)x(center of gravity of car for weight)