Method of Sections
The Method of Sections approach to truss analysis is a little more complicated than is the Method of Joints. It considers the reactions at the supports, a sign convention when summing vertical and horizontal forces and the removal of a cut section to determine the internal stress in the remaining individual members.
The Method of Section is a quick alternative to the 'Method of Joints' and the 'Maxwell Diagram'. It is an analytical process, which reinforces the concepts of Bow's Notation, Reactions at Supports and Static Equilibrium.
Principles:
* This process allows individual members to be analysed without having to progress through each member in turn.
* An incorrect 'sense' assumption is revealed by the final answer; i.e. a negative answer indicates an incorrect 'sense' choice.
Example: Use the ‘method of section’ process to calculate the forces in the members indicated. The truss is in static equilibrium and the reactions at each support are vertical.
space diagram
You are to find the forces in top chord and the inclined member when the reaction at the right support is 450 kN ( and the vertical members are ‘redundant’.
Analysis:
The truss is in equilibrium and therefore the moments caused by the forces in all members are in equilibrium.
When a moment is taken about a joint through which a member passes, there can be NO moment for that member.
In the case here, a positive result indicates that the member is in Tension and conversely, a negative result indicates Compression.
The vertical height of the truss is 3.5 m.
To find the top chord 4,5; force ‘x’
(-450 x 7) + (-X x 3.5) = 0
-X = - 3150
3.5
= 900kN
= 900 kN i.e. compression
To find the inclined member 5,7; force ‘y’ you must sum the vertical forces.
Σ FV ( = 0
y sin 45( + 450 = 0
y = - 450
sin 45(
= - 636.39 kN
= 636...