Fundamentals of Structural Engineering

End Reactions

BeamsA beam is a horizontal or inclined member that carries a load and is supported at two or more points.

Reactions

Reactions are the forces acting at the supports of the beam. The reactions resist the beam load and hold the beam in equilibrium.

LoadsThe two most common types of loads considered in design are dead loads and live loads.

Dead loads are loads that remain essentially constant after they are applied. They include the weight of the beam, walls, partitions, floors, and other material which make up the finished structure.

Live loads are loads that vary. Live loads include loads from occupants of the building, elevators, machinery, traveling cranes, moving vehicles, and material or equipment stored in the structure. Other types of loads considered in design are wind loads, earthquake loads, and impact loads caused by machinery or moving vehicles.

Uniform LoadsA uniform load is a load that is uniformly distributed over a length of beam. Uniform loads are usually represented by closely spaced vertical lines as shown.

Concentrated LoadsA concentrated load is a load assumed to act at one point. A single vertical arrow indicates the location and direction of the load as shown.

Laws of EquilibriumReactions for different beam loads are calculated using the laws of equilibrium. These laws are based on the observation that if a beam does not move as loads are applied, all forces acting on the beam are in equilibrium, that is, they are balanced. The laws are expressed by the following formulas:

∑M = 0∑F (v) = 0∑F (h) = 0

Formula ∑M = 0 states that the algebraic sum (indicated by the symbol ∑ ) of the moments of all the forces equals zero.

Formula ∑F (v) = 0 states that the algebraic sum (indicated by the symbol ∑ ) of all vertical forces equals zero.

Laws of EquilibriumFor convenience, the vertical downward forces are considered negative and the vertical upward forces are considered positive.

MomentsA moment is the product of a force expressed in units of weight (kips) times a distance expressed in units of length (feet). The distance is the shortest distance (measured along a line at right angles to the force to the point about which the moment is taken (A). The numerical value of a moment is expressed in units of force and distance such as kip-feet.

Moments

For convenience in computation, moments tending to produce rotation in a clockwise direction are considered positive and those in a counterclockwise direction are considered negative.

Loading Diagrams

Steel DesignThere are currently two common methods of steel design:

The first (and older) method is the Allowable Strength Design(ASD) method.

Service loads and load combinations with a factor of safetyapplied to the resistance are used.

The second (newer) is the Load and Resistance Factor Design(LRFD) method.

Factored loads and load combinations with separate factors foreach load and for the resistance are used.

Steel Design

Steel Design