I've been asked to explain how monocoque chassis are designed. It's a bit of a challenger because the details of how a chassis is designed is dependent on the materials used and the application.
However, the overall basic principle is the same. A ship, an aeroplane and most race and road cars could all be described as monocoques. They are all made from relatively thin walls formed into shapes, or supported by other elements to provide strength and stiffness.
A cardboard box is a form of monocoque, in that it had thin walls, and is only a rigid structure when the ends are folded to close the box off. What happens in the case of the box is that you have a shear plane on each face of the box and therefore you have a shear panel in each of the principle directions so that the box can't easily deform. In vehicles you will have a floor, sides, front and rear bulkheads and in a lot of cases a roof to form the enclosed stiff structure.
The problem comes when parts of the system feed loads directly onto these thin walls, obviously there is no stiffness there, so in order to stiffen the panels at the points that these loads are applied, by adding in bulkheads (to form an extra shear web). These don't always need to be full bulkheads, but they can be box section elements to help stiffen the panel, and direct the loads into surrounding panels.
For example an average car is made from sheet steel about 1mm thick, and if you ever try to handle a 1mm thick sheet of steel you'll see it's incredibly hard to handle. But fold a simple return flange around the edge even only a few mm's thick and it's stiffness increases dramatically. The floor of a car is essentially a sheet of steel, so it's not at all stiff until they fold it around the edges to form the sills, and they will form rib shapes into the footwell areas, and normally form or spot weld on a tunnel section where the gearstick and hand brake lever will fit. Normally they'll be a boxy section under the rear seats. There are plenty of pictures of floors and other car chassis parts being stamped online and no doubt on YouTube to give you a clearer idea of the sort of shapes and forms they add to the floor in order to make it stiffer. The rest of the cars chassis is similarly designed so that panels, folds and stamped forms add stiffness to the basic panel, before it all comes together to add stiffness and strength to each other sub-structure.
To simplify it further take a look at the common beam bending equations. Far and away the most important aspect of how much a beam bends or twists is the sectional properties of the shape. In bending that's I and in torsion J. If a car is to be stiff in beaming, then the general cross section needs to have a large Ixx value, and large Ixx values come from having the walls a long way the neutral axis, and from having lots of walls that are in the shear plane of the load. So for a car, you have a large approx. square shape, with a two extra shear webs from the tunnel in the middle and another couple of small shear webs formed by the hollow sills on the outside edges of the floor.
In a F1 car you have the same principles at play, except the Carbon fibre material used gives you a greater degree of control of the material properties. An F1 car is not actually all that stiff in comparison to a road car, and racing car with a roll cage in a production shell will often exceed the torsional stiffness figures of an F1 monocoque. This is primarily because of the Ixx value that you can achieve from the much larger cross section of a typical road car. However where an F1 monocoque wins is in it's stiffness to weight ratio.
Carbon monoques are have walls made of two skins of carbon fibre sandwiching a honeycomb material, which is usually aluminium. The aluminium honeycomb is nothing more than a thin foil maybe less than 0.5mm thick formed into hexagonal cells. The honeycomb comes in sheet form and typically F1 cars use about 10mm thick honey and 2-2.5mm thick carbon walls. Carbon fibre cloth is approx 0.2mm thick so you have to lay up around 10 sheet of carbon (termed plies) to form one wall. This sandwich structure forms exceptionally light and yet stiff walls for the monocoque. Far stiffer than the thin sheets of steel, and so you don't always need to make use of shape and bulkheads and other supporting structures in the same way as you would with steel. However, like any material if you try to put point loads directly into the walls of the carbon monocoque you'll have problems. Carbon is very brittle and you'll crack the skin of the monocoque unless the skin and wall is properly supported.
In a F1 monocoque in areas where they need to attached components like the suspension directly to the outside of the monocoque they be a solid carbon or metal insert replacing the honeycomb in the wall structure. In the case of suspension parts the walls will need added support and you'll find some bulkhead structure behind the inside wall to provide support. There is a great YouTube clip showing the layout of a Sauber F1 monocoque where the chassis is cut in half so you can see everything inside. This clearly shows where the bulkheads and other shapes and features are that support the outer walls when there are loads that require the added support.
A company called Hexcell composites have a great website where you can download a lot of details about working with their pre-made honeycomb sandwich boards. A lot of the techniques they describe in that documentation are used in vehicle composite structures.
With carbon composite monocoques you have the advantage that you can vary the material properties at any point on the chassis to aid stiffness, strength or support for other elements. You can thicken the area by adding more plies of carbon cloth, you can vary the orientation of the cloth so that more of the carbon fibres are aligned with the direction of the resulting load thus stiffening that area, or you can use Uni-direction cloth which has all the fibres runnin in a single direction, thus meaning that you can put all of the carbon to work in the direction of the load. Usually a carbon monocoque will be made of a mixture of cloth and uni-directional (UD) fibres. The UD plies are often wrapped around the chassis at approx 45 degree angles to help provide extra stiffness in torsion, and the woven cloth will be orientated differently through each ply and sandwiching the UD in order to support the UD fibres and provide a more universal load carrying capability.
Saying all of that, everything basically boils back down to the simple cardboard box concept, of thin walls supporting other thin walls.
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