Theory of Structures - Beams Vocabulary (From Lecture Notes)

Vocabulary flashcards covering key beam theory concepts, standard formulas, and methods from the lecture notes.

Simply Supported Beam

Beam supported at ends by simple supports (pins/rollers) with no fixed end moments.

Mmax (Simply Supported under UDL)

Maximum bending moment under a uniform load on a simply supported beam; occurs at midspan: Mmax = wL^2/8.

Vmax (Shear in a Simply Supported Beam under UDL)

Maximum shear force; each support carries a reaction of V = wL/2.

δmax (Deflection in a Simply Supported Beam under UDL)

Maximum vertical deflection; δmax = 5 w L^4 /(384 E I).

Cantilever Beam

Beam fixed at one end and free at the other.

Mmax (Cantilever with Point Load at Free End)

Maximum moment at the fixed end: Mmax = P L.

δmax (Cantilever with Point Load at Free End)

Deflection at the free end: δ = P L^3 /(3 E I).

Mmax (Cantilever with Uniform Load w)

End moment at the fixed end: Mmax = w L^2 / 2.

δmax (Cantilever with Uniform Load)

Deflection at the free end: δ = w L^4 /(8 E I).

Equal Span Continuous Beam

Beam with two equal spans continuous over a middle support; maximum negative moment at exterior supports: Mmax = MAB or MBC = 9 w L^2 / 128, located at 3/8 L from exterior support.

Mmax Location in Equal Span Continuous Beam

Maximum moment occurs at 3/8 of the span length from the exterior support.

Interior Support Reactions in Equal Span Continuous Beam

Reactions: RA = RC = 3/8 w L; RB = 5/4 w L (for the typical equal-span continuous beam under UDL).

Propped Beam

Beam with a prop providing an additional support; yields a negative moment at an interior support (M_AB = 9 w L^2 / 128, located at 3/8 L from support B in the notes).

Mmax for Propped Beam under Uniform Load

Maximum moment magnitude for a propped beam under UDL: M_AB = 9 w L^2 / 128 at 3/8 L from exterior support.

Fixed-Ended Beam

Beam fixed at both ends (built-in) with no rotation at supports.

End Moments for Fixed-Ended Beam

Under UDL, MA = MB = w L^2 / 12 (sign depending on convention); midspan moment M_mid = w L^2 / 24.

Three Moment Equation

Clapeyron’s theorem relating bending moments at three consecutive supports in a continuous beam; used to determine unknown end moments.

Conjugate Beam Method

A deflection-analysis method using a conjugate beam whose bending moments correspond to the slopes of the original beam to compute deflections.

Backup Methods (Three Moment Equation or Superposition)

Alternative approaches for deriving deflection and moment relations in simple and continuous beams, including using the three-moment equation or superposition.