plane trusses

Plane Trusses

Plane Truss: Layout

Objective - Determination of Internal Forces

Definition/Properties Internally Static Determinacy The Method of Joints The Method of Sections

objective [ b'd ektiv] ə ʒn. 目的；

joint[d nt]ʒɒɪ 节点 section ['sek n] ʃən. 截面；

Bridge Truss Structures: Bridge

Truss Structures: Roof

Commonly Used Roof Trusses

roof [ru:f] n. 屋顶；

Truss: Definition

Straight Members Pin-jointed Loaded at JointsWeights ignored No-collapsible (rigid)

collapsible [k 'læps bl]ə əadj. 可折叠的；可变形的

Truss: Rigid or Collapsible

Basic Rigid Form(No-collapsible)

Collapsible Form(Mechanism)

Simple Truss

Two-Force Member & Internal Force

The Same Internal Force (T/C) at all sections

The Method of Joints

Determine the internal forces in all three members.

The Method of Joints: Procedures

Check Static Determinacy: Externally & Internally Determine the External Reactions (r=3)– FBD of the whole structure; Apply ΣFx=0; ΣFy=0; ΣM=0 Choose a Start Joint–Only two unknowns/members at the joint; – Apply Σ Fx=0; Σ Fy=0 Design a Joint Visit Order–Make sure no more than two unknowns need to be found

when visiting a particular joint;– Apply Σ Fx=0; Σ Fy=0 Check the Results by Employing Unused Joints or Equati

ons, if Possible.

The Method of Joints: Example II

Determinate the force in each member of the

loaded simple truss.

All triangles are equilateral

triangle ['traiæ ɡl] ŋn. 三角（形）；

II: Find External Reactions

I: Check Static Determinacy

1. r=3, so externally s.d.2. m=7, j=5; m+r=2j; so internally s.d.

III: Joint Visit Order

IV: Joint Analysis (1)

IV: Joints Analysis (2)

The Method of Joints: Example III

Determinate the force in each member of the loaded simple truss.

The Method of Joints: Example IV

Determinate the force in each member of the loaded simple truss.

The Method of Joints: Example V

Compute the forces in members BC, BE and EF of the loaded truss.

Joints Visit Order

The Method of Sections

Method of sections

The Method of Sections: Example V

Example VI

Compute the force in member DJ.

Advanced Issues

Externally Static Determinacy (Refer to Example IV)

Use of Two or More Moment Equations

Choose a Local Coordinate System

local ['l uk l] ə ən. 局部；

adj. 当地的；局部的；

coordinate [k u' :dinit] ə ɔn. 坐标；

Advanced Issues: Example VII

Compute all member forces. All inclined members are at 300 or 600.

Local Coordinate Systems

Advanced Issues: Example VII