Northing-Easting Method of Truss Analysis · after the 2012 workbook by Eng. Prof. Duwa Hamisi Chengula, Mbeya University of Science and Technology (MUST)
| Name | Easting x (m) | Northing y (m) |
|---|
| From | To | Length | Bearing θ | EA |
|---|
Bearing is measured clockwise from North, from the first joint to the second — the same angle the workbook's “Angles” sheet produced. EA (relative axial stiffness) matters only when the truss is statically indeterminate; leave it at 1 for equal members.
| Joint | Type |
|---|
Reactions are named as in the workbook: H = horizontal (positive East), R = vertical (positive North).
| Joint | Force (kN) | Bearing θ (°) |
|---|
Direction the load points, clockwise from North: 180 = downward (gravity), 90 = East, 270 = West, 0 = upward.
Your current truss is kept in this browser automatically. To keep a copy elsewhere, copy the project data and paste it into a text file; to open one, paste it below or choose the file.
The model on the first tab worked by the Northing-Easting Method of Truss Analysis, as in the workbook: every member and force is given a bearing θ measured clockwise from North, resolved into its Easting (F·sin θ) and Northing (F·cos θ) components, and the two equations ΣFE = 0 and ΣFN = 0 are solved at each joint by Cramer's rule — reactions first, then each joint with no more than two unknown members.
The model on the first tab solved by the direct stiffness (displacement) method. The unknowns are the joint displacements rather than the member forces, so the same steps work for determinate and indeterminate trusses. Directions follow the program's convention: x = East, y = North, and each member's direction comes from its bearing θ (λx = sin θ, λy = cos θ).
A direct copy of the workbook's “Analysis of Member Forces” sheet. For each joint, enter up to three known forces and the joint loads, then name the two unknown members and their bearings. In a force box you can type a number or the name of a member solved in an earlier joint (for example CB — the reversed name BC also works).
The Northing-Easting Method of Truss Analysis (Eng. Prof. Duwa Hamisi Chengula, 2012) analyses a pin-jointed truss joint by joint using bearings measured from North and force components along the Northing and Easting axes. The rules below are carried over from the workbook's user manual, with notes on how each part of this program applies them.
Truss model. Enter joint coordinates (Easting, Northing in metres), connect them with members, add supports and joint loads. The truss is solved as you type by writing the two equilibrium equations ΣFE = 0 and ΣFN = 0 at every joint and solving them together. The program checks m + r against 2j (members + reactions vs twice the joints): equal means statically determinate; fewer means unstable; more means statically indeterminate, which is then solved by the stiffness method using each member's EA — the job the workbook's unit-load sheet did for a redundant member.
Northing-Easting method. A printable record of the Northing-Easting Method of Truss Analysis for the same truss. Where no joint has two or fewer unknowns left (a truss that needs the method of sections), the working says so and takes the one extra value it needs from the simultaneous solution, then carries on.
Joint calculator. The original sheet, one joint at a time, for checking hand calculations or working a truss you have not drawn.
FE = F·sin θ · FN = F·cos θ
Example: a 10 kN gravity load has θ = 180°, so FE = 0 and FN = −10 kN.