Trusses are used to support roofs
strengthen bridges
or support towers
the basic question
why should we analyze a truss ?
this is because if you want to design truss members
and it's joints properly
you should have clear knowledge of what is the load carried by each member of
the truss
under a given loading condition
before going to truss analysis
let's see the main assumptions behind it
truss members are connected at their ends only, and they're connected by frictionless pins
so you don't have to consider any secondary bending moment induced due
to force friction
next assumption is that, truss is loaded only at the ends
and the last one is, weight of truss members can be neglected compared to
load acting on it
force developed in a truss members is always axial
it can be either tensile or compressive
If a member is under tensile load this'll be the direction of internal force
developed
so you can notice that
under tensile load
internal force developed in truss member is directed away from the joint
similarly in case of compressive force the internal force developed in the
member is directed towards the joint
the most common way to determine forces inside a truss is, Method of Joints
The basic concept behind method of joints is that
since the trusses in equilibrium
each joint in truss will also be in equilibrium
the procedure for method of joint is as follows
first step
Determination of reaction forces
for this purpose we can use three equilibrium equations of truss
that is sum of horizontal forces is zero. Sum of verticle forces is zero
and moment acting any point in trust is zero
after determining the reaction forces next step is to apply a concept of equilibrium of joint
consider joint where there are not more than two members
in which forces are unknown
two unknowns because
we have only got two equations of equilibrium to solve them
joint is in equilibrium in X direction and joint isn't equilibrium in Y direction
So we can solve for both the unknown forces
Please note that we cannot use equilibrium of moment
because moment produced by member forces in a joint is zero
Since all forces are passing through the same point
Once you're done with one joint you can move to the next joint
and do the same analysis there
the procedure is repeated till we have solved all the unknown forces in truss
Nnow let's do a sample problem
truss analysis of following structure
which is used to lift weight
one end of that is connected to a roller and other end to a pin
So first step
Determination of reaction forces
from free body diagram
since one and is connected by a roller reaction force will be purely vertical
at the other end
both vertical horizontal reaction forces are present
as the whole structure is under static equilibrium
we can use three equilibrium equations to solve for
three component of reaction
now analysis at each joint
Let assume that all members are under tension.
So forces are moving away from joint
Internal forces developed and number of unknown forces around each joint is as
shown here
it's clear that we could start our analysis from joint A or from joint D
both are having two unknowns
other joint are having three unknown forces each
let's start with joint A
Forces in both members can be solved using the equilibrium formulae
If sign of any force comes negative
that means that member is under compression
Now we can move to point B
there number of unknowns are 2 now
using the same concept we can solve for forces in members 3 and 5
now the only unknown force remaining is at member 4
which can be easily solved by considering equilibrium at point C or D
just by considering one equilibrium equation
Hope you have a good understanding on structural analysis using method of joints
thank you