Method of Sections

Method of Sections

Method of Sections allows us to calculate unknown internal forces inside of Warren Truss. (usually), and determine whether they are in Compression, or Tension.

Page 137 in the book

Important Stuff

From this line in the syllabus;

Syllabus

“The Moment Arm, not the force, shall be the variable requiring trigonometry in determining any particular moment required.”

From this it sounds sort of like we shouldn’t use ∑FH\sum F_H and ∑FV\sum F_V, and this is supported by the exam answers, only having answers listed for solving with moments however, the latest 2022 exam uses ∑FV\sum F_V in the answer key, and it’s not like it wasn’t a viable option in the 2019 exam, I can solve that question in 3 different ways while still getting the same answer, the way they did it, with moments, just so happens to be the most complicated one, and that question is awarded 6 marks because of it, where-as using ∑FV\sum F_V makes it trivial, they do not indicate any-where that you cannot just use ∑FV\sum F_V.

Mr. Milne said exam answers are just intentionally vague so markers have leeway, so the syllabus quote probably only actually applies to when your finding the moment of an intenral force on a slant, or maybe just doesn’t matter at all.

Lines of Action & their Moment Arms

The Line of Action is a imaginary, often dotted line that extends directly forward, and forever backward from the force of interest out to (I assume?) infinity.

In the equation for a moment, M=F×DM=F \times D;
DD measures the Length of the Moment Arm, the moment arm travels perpendicular to the Line of Action towards the Moment-taking point. If a force’s line of action passes directly through your current moment-taking point, there is no perpendicular distance to travel, it has already arrived at it’s destination, D=0D=0 and so the moment will equal zero when ∑M\sum M, the moment is Eliminated, and no turning effect is generated.

Eliminating Forces

You can take advantage of this to eliminate unknowns from the Equation of moments, as seen below.

^ don’t do that

Eliminated unknown forces about Y, are dark red and so are their lines of action.

When solving, horizontal and vertical forces are really easy because the moment arm, will just swap between Horizontal and Vertical.

  • Perpendicular to Horizontal is Vertical
    • Vertical Forces are measured by their Horizontal Distance, because that Horizontal Distance is the moment arm.
  • Perpendicular to Vertical is Horizontal
    • Horizontal Forces are mea sured by their Vertical distance, because that Vertical distance is the moment arm.

The moment arm can come from anywhere on the line of action.

So long as moment-taking point and force are on the same structure, the moment arm will just find any point on the Line of Action, where it can be perpendicular to the Line, and intersect with the Moment-taking point.

The perpendicular distance from Y, to the line of action is dark purple, “2.121m”. In this one it was literally just pythag to find the hypotenuse of the triangle.

Struts & Ties

A particular member can either be in

  • Compression (Strut)
  • Tension (Tie)

Idk if the definition of Tension or Compression really matters, just assume tension, if the answer comes out as a negative, say it’s in compression and change the arrows.

The Actual Method of Sections

Some parts, (mainly things in warning boxes) may be slightly out of context.

Since I first did this part after first learning M.o.S and have re-done it 2-3 times since

First we must cut through the unknown forces with a section line.

Then we assume the “sense” of the members, conventionally, we assume they are in Tension. then if we solve it and the sign is negative, then we flip it to compression.


We can then use the Equilibrium Equations to solve for the Internal Forces inside each of the members.

Finding FGDF_{GD}

We can use the Moments Equation to find FGDF_{GD}

Finding FBFF_{BF}

Using Sum of Horizontal Moments

Horizontal Moments

Finding FFGF_{FG}

Sum of moments except you violate the syllabus, and resolve it first.

Using sum of Vertical Moments (again? idk how i did this twice, this ones older tho)

Vertical Moments (again? idk how i did this twice, this ones older tho)

Extra Notes

Reference Video ( … s)

Video ( … s)