Structures

Part of the Statics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal

Lecture

Structural engineering relies heavily on the strengths of materials and their ability to withstand forces of tension or compression. When used in conjunction with each other, as in the case of a truss, individual load bearing members both share and transmit loads, enabling the structure to accomplish much more than any individual member could alone.

Plane Trusses

One way of distributing a force across a large distance is by building a Plane Truss, which takes advantage of the principle of Equilibrium to translate forces along a system of interconnecting members.

A Warren Truss

A Pratt Truss

File:Simpletruss.PNG

A Simple Triangle Truss

The simplest truss is a triangle made of three points: A, B and C, and three members: AB, BC and CA. The method of distributing forces amongst many members relies on the engineer's ability to place a tensile or compressive force at any particular location. To properly sum forces at a particular point, one must be able to sum forces into that point and also away from it. Thus, AB and AC are in compression while BC is in tension.

Method of Joints

File:TrussJoint.jpg

The principle of equilibrium is only effective when applied to a single point. Therefore, the Method of Joints is applied to a truss-joint to determine the forces in each member of the truss. A place where the forces and members meet becomes the joint to be examined, and the principle of equilibrium is applied, thus solving the question of where the forces are transmitted in that truss around that joint.

Example: Consider a truss bridge with a load <math>\vec F_y</math> at point A. What resultant force <math>\vec R </math> acts upon the bottom the bridge?

Equilibrium dictates that <math> \sum \vec F \ = 0 </math> and <math> \sum \vec M \ = 0 </math>

Therefore, if AB, BC and CA are of equal length L...

<math> \sum \vec M_E \ = \vec F_y * L = 0 </math> and <math> \sum \vec F_y \ = \vec R - \vec F_y = 0 </math>, so <math> \vec R = \vec F_y </math>

Assignments

Activities:

• Create an activity

Readings:

• Peruse the appropriate sections of Wikibooks:Statics
• Introduction to Structural Design, Virginia Tech.

Study guide:

1. Wikipedia article:Plane Truss
2. Wikipedia article:Tension
3. Wikipedia article:Compression
4. Wikipedia article:Method of Joints
5. Wikipedia article:Method of Sections