look also at the 100x50x2mm tube, which has 93
per cent of the strength of the 75x50x5mm size,
but nearly half its weight! And I’ve thrown in the
50x50x2mm RHS to show how quickly strength
falls away with reducing depth of section. It has
only 18 per cent of the strength of its 100mm-deep
cousin. That’s because the strength formula has
a ‘depth cubed’ function in it.
What I’m trying to persuade fabricators to do
is to use depth of section to their advantage,
not wall thickness. We all know that when we
cut away the floor panels of a uni-construction
vehicle there is nothing thicker than 2mm in the
structure we remove, so why put 3mm, 4mm or
even 5mm-thick materials back in there? It’s not
smart.
I often see where the vehicle fabricator/modifier
has notched a section of chassis or crossmember
to allow the exhaust to pass through or for more
diff travel under the chassis. They often ask if they
can put some vertical gussets inside the chassis
to make up for the notch, but that’s just putting
back the material that the clever engineers
realised was doing nothing. It doesn’t fix the
loss of depth. Adding inefficient material might
regain 10 per cent of the loss of strength. They
might then ask if they can put some fish plates
on the outside of the notch to fix it. That solution
doesn’t give any more depth to the section either.
Fish plates will typically improve the strength
result only by 10-15 per cent. The strength of a
rectangular section in bending is a depth cubed
function, so any loss of depth accentuates the
strength reduction.
The best solution is to design the modification so
that notching a structural member is not required.
The shape of the chassis can be changed in the
problem area so that it retains its structural size
but provides room for the component requiring
that space.
The next best solution is to replace the material
that is taken out via the notch and put it on top
of the section so that the depth is restored. This
is often successfully done on rear suspensionnotches where the material can disappear inside
the body.
Similarly, for round tubes, diameter wins over
wall thickness for strength and mass efficiency,
but in this case the strength formula in bending
is a ‘diameter squared’ function instead of ‘depth
cubed’.
Finally, let’s look at the big picture of strength
in terms of depth. For a mono-construction car
body, the depth of the whole body section is
what determines its strength. Taking the front
subframe, for example, we know that when we
space-frame out the engine compartment the
strength of that area is no longer just that of the
rectangular main rails; it’s the depth of the whole
frame. This fabricated structure is then capable
of absorbing much higher engine loads and
spreading them to the strong cabin area.
It’s simply smart engineering to use depth of
section in designing modifications in order to
maximise strength while keeping weight down
for performance. sRHS size kg/m Moment of inertia Strength ratio
100 x 50 x 2mm 4.5 7.75E-07 93.00
75 x 50 x 5mm 8.35 8.35E-07 100.00
75 x 50 x 3mm 5.42 5.50E-07 66.00
75 x 50 x 2mm 3.72 3.85E-07 45.00
50 x 50 x 2mm 2.93 1.47E-07 18.00
TABLE 2: RECTANGULAR HOLLOW SECTION
TABLE 1: NEUTRAL AXIS
Neutral
axis – no
stress
Compression
Tension
Fibres longer
Fibres shorter