Theory of Structures 2 - Influence Lines and Deflections

Vocabulary and formula review flashcards for Theory of Structures 2, covering truss influence lines and superposition method beam deflection equations.

Influence Line for Truss

A representation of structural response at a specific point (such as a member force) calculated as a unit load moves across every joint of the structure.

Maximum Deflection of a Cantilever Beam with End Moment

$$\delta_{max} = \frac{M L^2}{2 E I}$$

Maximum Deflection of a Cantilever Beam with Point Load at Free End

$$\delta_{max} = \frac{P L^3}{3 E I}$$

Maximum Deflection of a Cantilever Beam with Uniform Load

$$\delta_{max} = \frac{w L^4}{8 E I}$$

Maximum Deflection of a Cantilever Beam with Triangular Load

$$\delta_{max} = \frac{w L^4}{30 E I}$$

Maximum Deflection of a Cantilever Beam with Point Load at Distance $a$ from Support

$$\delta_{max} = \frac{P a^2 (3 L - a)}{6 E I}$$

Maximum Deflection of a Simply-Supported Beam with Point Load at Midspan

$$\delta_{max} = \frac{P L^3}{48 E I}$$

Maximum Deflection of a Simply-Supported Beam with Uniform Load in Entire Span

$$\delta_{max} = \frac{5 w L^4}{384 E I}$$

Maximum Deflection of a Simply-Supported Beam with Two Point Loads at Middle-Thirds

$$\delta_{max} = \frac{23 P L^3}{648 E I}$$

Maximum Deflection of a Simply-Supported Beam with Three Point Loads at Quarter-Points

$$\delta_{max} = \frac{19 P L^3}{384 E I}$$

Maximum Deflection of a Fixed-Ended Beam with Point Load at Midspan

$$\delta_{max} = \frac{P L^3}{192 E I}$$

Maximum Deflection of a Fixed-Ended Beam with Uniform Load in Entire Span

$$\delta_{max} = \frac{w L^4}{384 E I}$$

Maximum Deflection of a Propped Beam with Uniform Load in Entire Span

$$\delta_{max} = \frac{w L^4}{185 E I}$$

Maximum Ordinate for Influence Line of Member CD (Practice Problem 1)

$$0.75$$