Constructing Influence Lines for Structural Analysis: A Step-by-Step Guide, Slides of Design

Download Constructing Influence Lines for Structural Analysis: A Step-by-Step Guide and more Slides Design in PDF only on Docsity! Constructing Influence Lines Steven Vukazich San Jose State University In addition to supporting fixed gravity loads (Dead Load), structures must also support gravity loads that can vary in magnitude and position (Live Loads). To design the components of a structure, it is important to understand how to place live loads to produce the maximum response for important design quantities (e.g. support reactions, internal shear, bending moment, axial force). Why Do We Construct Influence Lines ? The Influence Line for a response quantity is a tool to help place live loads to find the maximum response Choose Reference Coordinate and Sign Convention The overhanging beam shown has a fixed support at A, a roller support at C and an internal hinge at B. Construct influence lines for: 1. The roller support at C; 2. The vertical reaction at the fixed support at A: 3. The moment reaction at the fixed support at A 9 m 6 m 3 m D C B A x ++ Sign Convention for Positive Support Reactions Place Unit Load at x = 0 (Point A) 9 m 6 m 3 m D B x Free-body Diagram Ax Ay Cy 1 MA 4 Unknowns – 3 Equations of Equilibrium Need to make a cut at the hinge at B Place Unit Load at x = 0 (Point A) 9 m 6 m 4 m D B x Free-body Diagrams Ax Ay Cy 1 MA 6 Unknowns – 6 Equations of Equilibrium B VB VB FB FB "𝑀$ = 0+ "𝐹) = 0+ "𝐹* = 0+ Cy = 0 FB = 0 VB = 0 "𝑀+ = 0+ "𝐹) = 0+ "𝐹* = 0+ MA = 0 Ax = 0 Ay = 1 Place Unit Load at x = 12 m 3 m 6 m 3 m D B x Free-body Diagrams Ax Ay Cy 1MA 6 Unknowns – 6 Equations of Equilibrium B VB VB FB FB "𝑀$ = 0+ "𝐹) = 0+ "𝐹* = 0+ Cy = 0.5 FB = 0 VB = 0.5 "𝑀+ = 0+ "𝐹) = 0+ "𝐹* = 0+ MA = – 4.5 m Ax = 0 Ay = 0.5 9 m Place Unit Load at x = 15 m 3 m 6 m 3 m D B x Free-body Diagrams Ax Ay Cy 1MA 6 Unknowns – 6 Equations of Equilibrium B VB VB FB FB "𝑀$ = 0+ "𝐹) = 0+ "𝐹* = 0+ Cy = 1 FB = 0 VB = 0 "𝑀+ = 0+ "𝐹) = 0+ "𝐹* = 0+ MA = 0 Ax = 0 Ay = 0 9 m Place Unit Load at x = 18 m 6 m 3 m D B x Free-body Diagrams Ax Ay Cy 1 MA 6 Unknowns – 6 Equations of Equilibrium B VB VB FB FB "𝑀$ = 0+ "𝐹) = 0+ "𝐹* = 0+ Cy = 1.5 FB = 0 VB = – 0.5 "𝑀+ = 0+ "𝐹) = 0+ "𝐹* = 0+ MA = 4.5 m Ax = 0 Ay = – 0.5 9 m