trusses are used to support roofs strengthen bridges or support towers the basic question why should we analyze a truss ?
woodworking joints diagrams, this is because if you want to designtruss members and it's joints properly you should have clear knowledge of whatis 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 endsonly, and they're connected by frictionless pins so you don't have to considerany secondary bending moment induced due to force friction next assumption is that, truss is loadedonly at the ends and the last one is, weight of trussmembers can be neglected compared to load acting on it
force developed in a truss members isalways axial it can be either tensile or compressive if a member is under tensile load this'llbe 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 forcethe 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 isthat since the trusses in equilibrium each joint in truss will also be inequilibrium the procedure for method of joint is asfollows first step determination of reaction forces for this purpose we can use threeequilibrium equations of truss that is sum of horizontal forces is zero.sum of verticle forces is zero
and moment acting any point in trust iszero after determining the reaction forcesnext 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 ofequilibrium to solve them joint is in equilibrium in xdirection 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 forcesin a joint is zero since all forces are passing throughthe same point once you're done with one joint you canmove to the next joint and do the same analysis there the procedure is repeated till we havesolved 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 rollerand other end to a pin
so first step from free body diagram since one and is connected by a rollerreaction 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 undertension. so forces are moving away from joint internal forces developed and number ofunknown forces around each joint is as shown here it's clear that we could start ouranalysis from joint a or from joint d both are having two unknowns other joint are having three unknownforces each let's start with joint a forces in both members can be solvedusing the equilibrium formulae
if sign of any force comes negative that means that member is undercompression now we can move to point b there number of unknowns are 2 now using the same concept we can solve forforces in members 3 and 5 now the only unknown force remaining isat member 4 which can be easily solved byconsidering equilibrium at point c or d just by considering one equilibrium equation hope you have a good understanding onstructural analysis using method of joints
thank you