Method of Joints

What Do you Mean by Method of Joints?

The method of joints is a technique for figuring out the forces unknown to the members of a truss. The technique is frequently the quickest and simplest way to solve all the unknown forces in a truss structure since it focuses on the joints or connection points between the members.

A common assumption in truss analysis is that loads are imposed only at joints and not at intermediate places along the members. The members’ weight is sometimes ignored because it is negligible compared to the applied loads; as an alternative, the two end joints of each member may support half of its weight. If the members are long and thin, the moments conveyed via the joints are minimal, and the junctions can be thought of as hinges or pin joints because of this.

Truss

A truss typically comprises (but not always) straight components joined together at panel points. Due to the structural stability of that shape and design, triangles are frequently (though not always) used in trusses. The simplest geometric shape that won’t change shape when the side lengths are set is a triangle. In contrast, for a four-sided object to maintain its shape, its angles and lengths must remain fixed. The Munter Point is the term used to describe the connection where a truss is intended to be supported. There are three types of the truss as follows:

Simple Truss

A truss is a single triangle in its most basic form. This truss style is used in mechanical structures like bicycles and aircraft and framed roofs made of rafters and ceiling joists. A truss made completely of triangles is referred to as a simple truss due to the stability of this design and the analysis techniques used to compute the forces within it. However, a simple truss is frequently defined more narrowly by requiring that it can be built by adding pairs of members successively, each connected to two existing joints and to each other to form a new joint. This definition does not require a simple truss, only being made of triangles.

Planar Truss

A planar truss exists in only one plane. Bridges and roofs are frequently constructed using parallel rows of planar trusses. An effective structural form for trusses is the depth or the height between the upper and lower chords. A solid girder or beam of comparable strength would be heavier and more expensive to produce than a truss. A deeper truss will require more material in the verticals and diagonals and less material in the chords for a given span. Maximizing efficiency requires the truss to be at its ideal depth.

Space frame truss

A three-dimensional framework of members with pins at their ends is known as a space frame truss. The simplest space truss is a tetrahedron with six members that meet at four joints. Tetrahedrons with shared edges can be used to build massive planar structures, and they are also used to build the bases of large free-standing power line pylons.

Analysis of Truss

Trusses are structural systems composed of parallel; thin components joined at the ends. Axial tension or compression can be applied to truss members. Member’s axial compression is always seen as negative, but their axial tension is always regarded as positive. Trusses may be internally, externally, or indeterminately defined.

Trusses that can be determined using simply the equation for static equilibrium are said to be externally determinate. Trusses with an external unknown reaction are said to be externally indeterminate if the equilibrium equations cannot fully predict the reaction. Additional equations based on the compatibility of system components must be developed to determine the number of unknown responses over and above the equilibrium equation for the indeterminate trusses.

Analysis of Truss by Method of Sections

The method of sections is a technique for figuring out the forces unknown to the members of a truss. The technique entails disassembling the truss into separate portions and examining each section as a distinct rigid body. The method of sections is typically the quickest and simplest way to identify the unknown forces acting on a particular truss element.

• It is typically helpful to mark the truss members first. This will assist you in keeping things consistent and structured for later analysis.
• Draw a free body diagram, list the equilibrium equations, and solve for the reactive external forces operating on the truss system while treating the entire structure as a rigid body. A single rigid body analysis should not be different from this one.
• Next, visualize cutting your truss into two distinct pieces. As few members as feasible should be cut through for the cut to pass through the member you are attempting to solve for the forces. The cut doesn’t have to be straight.
• The last step is to build a free-body diagram for the two portions you established. Make sure to account for every force influencing each component.
• You made a free-body diagram for each area and wrote the equilibrium equations. You must draw down the force and moment equations because these will be extended bodies.
• Finally, find the unknowns in the equilibrium equations. You can solve for each variable individually using algebra or utilize matrix equations to solve for every variable at once. Recall that negative responses denote compressive forces in the members if you previously assumed that all forces were tensile.

Analysis of Truss by Method of Joints

The method of joints is a technique for calculating the internal axial forces present in a truss member. It entails moving through each truss’s joints one at a time, using equilibrium at each point to determine the unknown axial forces in the members attached to that joint. The methods below describe how to perform a 2D truss analysis using the method of joints:

• The techniques confirm that the truss is stable and determined.
• If truss members have zero forces, try to identify them to minimize the number of unknown forces.
• Using the equilibrium procedures covered in Section, determine the support responses for the truss.
• Determine the axial forces at a beginning joint with two or fewer members.
• To discover the unknown forces, create a free-body diagram of the joint and utilize equilibrium equations.
• Continue to the next joint if the axial forces are unknown and there are two or fewer members. Fix the joint’s unforeseen forces.
• Continue until all unknown truss member forces are identified.

Assumptions in Method of Joints

The truss analysis aims to determine member forces and reactions. the procedures for doing the analysis using the equilibrium equations and taking into account only a portion of the structure by examining its free body diagram to address the unknowns. The following are the assumptions made in the analysis of the truss.

• Members of a truss are only joined together at their ends.
• Frictionless pins are used to join trusses together.
• Only the joints are weighted in a truss structure.
• The weights of the members may be overlooked.
• All of the member’s bending resistance is negligible in contrast to their axial force resistance.

Method of Joints Problems and Solutions

Question 1:_______ is an analytical method for finding out forces in a frame.

Answer – Method of joints.

Question 2:In the joint method of plane truss analysis, the value of forces in the member of the truss can be found when the joint has:

Answer – Not more than two unknown force members.

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