Method of sections is a powerful tool to determine forces in statically determinate
plane trusses
Consider this problem
if you want to determine load in blue member, using method of joint
you have to proceed in following matnner
from one joint to another joint
in short you have to analyze 5 joints to determine force in a member
so you have to solve for ten equations
But using method of sections, just by solving three equations we can solve
load in any truss member. That's the power of method of sections
Steps involved in method of sections are as follows
First step determination of reaction forces
we can use three equilibrium equations of truss to find this
But for cantilever truss you can skip this step
Now the most important step
cutting the entire truss in to two parts by a section line
we'll learn how to draw a section line in coming sections
Third step is to apply the concept of equilibrium to any of the cut part
so that we can determine the member forces
The big question
How to draw a section line ?
Section line should pass through the members
whose internal force have to be determined
Section line should not cut more than three truss members. This is because we
have got only 3 equilibrium equations.
So we can solve only three unknown forces
Let's see few examples for drawing section lines
For this case if you want to determine force in member 1
we can draw the section line like this. This line is passing through only three
members, so this line is good
If you want to determine force in member 2,
we can draw section line like this. Here again the line is cutting
only three members
so we can solve for the unknown forces
In this cantilever example for determining force in member one
draw section line like this
now to find out internal unknown forces, you can separate out sections
Section at right hand side does not have a support
So if I apply concept of equilibrium to that section,
we need not solve for reaction forces
Assume all three internal forces are tensile in nature
since this section is under equilibrium
we can say sum of horizontal forces is zero
Sum of vertical forces is zero
and moment produced by truss forces at any point will be zero
Using these equations we can solve for 3 unknown forces
It's interesting to see that in method of sections, we can completely omit
effect of forces in uncut members
While solving if you get sign of any foce as negative
that means member is under compression
Now let's consider the previous example
The first step determination of reaction forces
from free body diagram
this section is good, it has got only three unknown forces
remaining procedure is same as the previous problem
before winding up the lecture let's summarize
advantages of method of sections
If you want to determine forces in few members instead of all the members you
can definitely go for method of sections.
Also if members are away from support you can go for this method
So it is obvious that method of sections is quick,
while method of joint is tedious
That's all about structural analysis using method of sections. Thank you !