Analyzing a 2-D Truss Structure by CAMERON KRAHN

Truss

ckrahn1 — 2021-03-11 19:28:36 UTC

A structure composed of slender members joined together at their endpoints.

Particle equilibrium

ckrahn1 — 2021-03-11 19:36:39 UTC

When the particle is not moving at all, and the sum of the forces is zero. The sum of the moments is also zero, because a particle has no tendency to rotate.

Rigid-body equilibrium

ckrahn1 — 2021-03-11 19:37:17 UTC

Rigid-body is in equilibrium when it isn't being translated or rotated. Take into account sum of forces, and moments in x and y. ALL forces and all their moments taken about any points is zero. These equations give 6 independent equations.

Reactions at support

ckrahn1 — 2021-03-11 19:37:41 UTC

Method of joints

ckrahn1 — 2021-03-11 19:38:05 UTC

Method of sections

ckrahn1 — 2021-03-11 19:38:34 UTC

When a body is in static equilibrium, every section of the body is also in static equilibrium

Determinate trusses

cdokken — 2021-03-11 19:39:26 UTC

2 equations

gscheidt — 2021-03-11 19:39:36 UTC

Sum of forces in x and y plane.

Making a cut

cdokken — 2021-03-11 19:39:53 UTC

We can make one or more a cuts through any section of a body, however, it is preferred if the cut only passes through three members

Which method to pick

cdokken — 2021-03-11 19:40:18 UTC

Zero force members

cdokken — 2021-03-11 19:40:38 UTC

Making sense of the results

cdokken — 2021-03-11 19:40:57 UTC

3 equations in 2-D

gscheidt — 2021-03-11 19:41:34 UTC

sum of forces in x and y, and sum of moments about x or

Determining Reactions

gscheidt — 2021-03-11 19:43:21 UTC

Reaction forces and moments will exist in the direction movement is restricted

cdokken — 2021-03-11 19:43:58 UTC

If you want to find the forces of only a few members of a truss use method of sections

cdokken — 2021-03-11 19:44:36 UTC

If you want to find all of the forces involved in a truss use the method of joints

gscheidt — 2021-03-11 19:49:06 UTC

Can be identified by treating a joint as a particle if you have 3 forces, 2 in alignment and 1 that is not

ckrahn1 — 2021-03-11 19:51:23 UTC

Members that support no loading, used to increase stability during construction and provide added support if the loading is changed.

Static Determinacy by counting

cdokken — 2021-03-11 19:55:18 UTC

(M+r) = 2j
M= Number of members
r= Number of reactions
j= Number of joints

cdokken — 2021-03-11 20:00:08 UTC

if (M+r) < r ---->partial fixity
if (M+r) < r ---->statically determinate IF fully fixed
if (M+r) < r --->Statically indeterminate

gscheidt — 2021-03-11 20:01:24 UTC

can use principles of particles of equilibrium by isolating a single joint and treating it as a particle

ckrahn1 — 2021-03-11 20:03:51 UTC

When using the method of joints, you start with the joint that has 2 or fewer unknowns, and step through the truss joint by joint.

gscheidt — 2021-03-11 20:07:40 UTC

A negative result indicates that a force acts in the direction opposite of its assumed direction

gscheidt — 2021-03-11 20:09:38 UTC

Tension is represented in FBDs by an arrow pointing away from the body of interest. Compression is indicated with an arrow going toward the body of interest

ckrahn1 — 2021-03-11 20:14:16 UTC

Created by:
Cameron Krahn
Greta Scheidt
Sahit Reddy
Connor Dokken