E1 Forces, Loads and Structural Balance

Topic

Every structural component must be in equilibrium: if the sum of the forces and moments acting upon it does not equal exactly zero, the component will not remain stationary but will instead move or rotate. This equilibrium is central to the module and represents the primary condition that any other structural mechanism in this catalog must satisfy.

Within this state of equilibrium, each material responds to applied force according to its own stiffness: within its elastic range, a material deforms in direct proportion to the stress it undergoes—a proportionality that distinguishes rigid steel from far more flexible wood under the same load. When a component undergoes bending, the resulting stress depends on two simultaneous factors: the bending moment and the distribution of the cross-section around the axis of bending; consequently, a deeper, better-distributed section can resist the same bending force using less material. This same stiffness and cross-sectional distribution determine the extent of deformation in a cantilever beam: such deformation increases rapidly with span length and decreases as the component becomes stiffer and better proportioned.

The loads testing this equilibrium are neither uniform nor constant: the structure's self-weight is fixed, whereas imposed loads, snow, and wind vary according to building type and climatic zone; structural equilibrium must support the combined effect of all these loads at all times. When a slender component is subjected to compressive loads, a failure mode other than material rupture may occur: a long, thin column can buckle laterally before the material's strength is exhausted. This critical buckling load depends on the material's stiffness, the cross-sectional distribution, and the component's length and end-support conditions. That is why this module—which opens with a summation of forces that must equal zero—concludes by showing that this same equilibrium can be disrupted in two very different ways: through excessive material stress or through the buckling of a slender member. Distinguishing which of these two threatens a given component forms the basis for all the structural design that follows in this catalog.

ID:4013