Pin-Jointed Frame Structures
A pin-jointed frame structure can be defined as a structure built up of a number of straight members connected together at their ends by frictionless pinned joints to form a stable geometrical arrangement which is capable of carrying loads applied at some or all of the joints.
Since each member has a pin joint at each end and a pin cannot transmit moment , then no member can transmit moment from one to another.
Force in a pin-jointed member must be axial.If the axial force is tensile,the member will increase in length under load and is called a tie.If the force is compressive ,the member will shorten and is called a strut.
If a frame has just sufficient members to be stable ,it is said to be a perfect frame and it is internally statically determinate.This means the internal member forces may be determined by repeatedly using the 3 equations for statical equilibrium.
We can know whether the plane frame is statically determinate by using the formula :
M is the number of members J is the number of joints
If M<(2J-3),THE FRAME IS NOT STABLE , it will COLLAPSE
If M>(2J-3),it is IMPERFECT and internally statically indeterminate.
Aside of the formula , the members must correctly positioned in the frame.
Since each member has a pin joint at each end and a pin cannot transmit moment , then no member can transmit moment from one to another.
Force in a pin-jointed member must be axial.If the axial force is tensile,the member will increase in length under load and is called a tie.If the force is compressive ,the member will shorten and is called a strut.
If a frame has just sufficient members to be stable ,it is said to be a perfect frame and it is internally statically determinate.This means the internal member forces may be determined by repeatedly using the 3 equations for statical equilibrium.
We can know whether the plane frame is statically determinate by using the formula :
M=2J-3
M is the number of members J is the number of joints
If M<(2J-3),THE FRAME IS NOT STABLE , it will COLLAPSE
If M>(2J-3),it is IMPERFECT and internally statically indeterminate.
Aside of the formula , the members must correctly positioned in the frame.
Method of Resolution at Joints
-Start at any joint that have no more than 2 unknowns
-Not necessary to determine the reactions before starting to resolve at the joints .
-If a joint without external load have 3 members,2 of the 3 are collinear ,then the third,non-collinear member must be zero.
-when the frame and loads are symmetrical , we only need to work halfway through the frame.
Method of Section
-To determine the value of a force in a particular member
-Cut the frame by a section through the member that you want to determine
-The maximum number of members that you can cut through is 3
-Solve the left or the right part of the frame in equilibrium.
-Take moment about the point of intersection of the line of action of 2 forces , so these forces do not appear in the moment equation and we can solve the remaining unknown force.
*Graphical method of solution is useful to solve frames which have a complicated geometry.
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