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In current terms, a pickup truck would be a much better example of a ladder frame than an SUV, since most current SUVs are unibody.

The information about aluminum in the second post is quite outdated and has some blatant errors. I suggest checking other sources for a more balanced view.

Backbone chassis

... this type of chassis is also often found on small sports cars.
It was, but not in recent decades. I can't think of a single one still in production, offhand; although of course I may have missed one or two, they're not common.

I am thinkin' about a backbone chassis design that incorporates the battery box as a structural member rather than something to be supported.

This way most of weight of the batteries could be centrally located & spread out along the length of the frame.
The driveline (the battery cables, speed controller & most of the wiring connections) could be mounted & ran thru the inside of the tunnel/tube & would be protected in the true spirit of a backbone chassis :D
I understand the logic, but it's hard to find enough space in a backbone box of reasonable dimensions to fit the entre battery; for instance, the Volt (which has only 16 kWh of capacity) fits only about half of the battery in the tunnel. To be workable, the backbone/box would need to be as long as possible, from nearly the drive axle to the other axle or even beyond.

The Bollinger 4WD, which is still really a concept at the stage, has a box beam backbone for most of the structure... but hangs the battery boxes off each side as seating area floor sections, with just motors and electronics within the backbone.
 

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Most of the vehicles with backbone chassis that I have seen, usually incorporate a differential & half shafts into the rear axle
By that, I assume that you mean an independent rear suspension and rear wheel drive. I agree, that's typical of the vehicles which have used backbone chassis.

But, I'm thinking of using a live axle on a light & balanced backbone chassis style kart
"Live axle" actually meant one which is driven - of any suspension design - but the use of the term has been distorted and now most people mean a driven (live) beam axle... and omit the "beam" part.

A backbone-style chassis is a strange combination with a beam axle (whether live or dead, with "dead" being not driven), since there is no need for structure near the centreline of the vehicle at the axle line with a beam axle, and yet there is a need for structure outboard for the suspension arms with a beam axle. The backbone puts all of the structure in the wrong place, so it would need to be extended nearly to the wheels on each side both at the axle line (for the springs and shocks) and further forward (in the case of a rear axle) for the control arm mounts.

I think that a backbone chassis with a beam axle is going to look more like a spaceframe in the back transitioning to a skinny (backbone) section in the middle of the vehicle, which would just be flexible (in torsion) and inefficient compared to a more normal spaceframe.

I realize that a live beam axle has a simpler driveline than an independent suspension. The simplicity results from fewer joints, with as few as two in the propeller shaft (driveshaft); a driven independent suspension typically has two joints per halfshaft, plus two or more in the propellor shaft (unless the engine or motor is at the axle line so there is no propeller shaft). Other than a couple of CV joints, what is the appeal of a live beam axle? It reacts to drive torque undesirably, and has high unsprung weight.

In an electrically-driven vehicle, the use of a live beam axle requires either:
  1. mounting the motor on the axle (like a typical golf cart), causing very high unsprung mass; or,
  2. mounting the motor remotely from the axle and using a propeller shaft (even though an independent suspension would allow the motor(s) to be directly coupled to the final drive).

The only live beam axle EVs in production for road use are adaptations of engine-driven vehicles with live beam axles - it's almost never the preferred configuration, especially for a sports car.
 

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It's probably helpful to think of dynamic loads as resulting from any acceleration of mass, rather than from movement (such as load shifting position in a truck); static loads are those seen under the influence of gravity but no acceleration.

Going over a bump accelerates the mass of the vehicle vertically (up, then down), so it causes dynamic loads.
Speeding up and braking are accelerating forward or rearward, so they cause dynamic horizontal loads through the suspension.
Going around a corner is accelerating sideways, so it causes dynamic loads through the suspension.
 

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I haven't dug into what you mean by "kart"; I've just been assuming some sort of non-roadgoing track vehicle with minimal or no bodywork... and not a classic "go-kart" or racing kart (which has no suspension and cannot use most of the discussed types of structure).

Some forum members have built small competition vehicles which might be similar to the intent in this case, for instance, the two by galderdi:
Autocross EV special
Aussie EV Autocross Special II

You might even be interested in the discussion in this thread:
fast mini buggy
It is for off-road use, but a track vehicle can be essentially the same thing, set lower and on different tires.
 

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If the kart seats two, it follows all of the usual structural and packaging considerations of a two-seat car.

If it seats only one (just the driver), then the situation changes. If you want the driver centred on the vehicle centreline, then a backbone chassis doesn't make much sense (since the driver would need to straddle the backbone). It is possible to build a single-seater with the driver on one side of the backbone and something (typically an engine, but in this case likely the battery) on the other side - the backbone can be offset somewhat (typically to give the driver a greater share of the body width).

galderdi's latest autocross special has some modules of the battery beside the driver's legs, but in spaceframe, not a backbone chassis.
 

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Nope, not planning for suspension on this one...
Then, as others explained, planned chassis flex is important. Tires form part of the virtual suspension too, but unless they are mushy off-road tires they won't provide enough compliance to work well.

A backbone of well-planned torsional stiffness (that is, not very stiff) can certainly work, but you need to be careful about where loads are attached to it.
 
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