Node method

The method of the nodes or method of the nodes, consists of the approach of mechanical balance of each of the nodes or knots of a simple reinforcement. A node is each of the points where two or more bars meet. The global balance of the structure implies the local balance of each of the nodes. For the node method to be applicable to a specific structure, some geometric conditions must be met, including:

• - That the structure has articulated nodes or behaves in a similar way to a structure of articulated nodes.

• - That the number of bars is less than a certain amount given by the number of bars:.

Zero force elements

The analysis of trusses by the "node method" is considerably simplified if we can first identify those elements that do not bear load. These zero-force elements are used to increase the stability of the truss during construction and provide additional support if the applied load is modified. Typically, the zero-force elements of a truss can be found by inspection of each of its nodes, making a free-body diagram of the truss and summing the forces. Typically, the zero-force elements are can be determined in the following ways:

• - If only two members form a truss and no extra load or support reaction is applied to the node, the two members must be zero force members.

• - If three elements form a truss node in which two of the elements are collinear, the third element is a zero force element as long as no external force or support reaction is applied to the node.[1]​.

This type of structures cannot be analyzed solely using the statics or equilibrium equations, since the latter provide an insufficient number of equations. Hyperstatic problems require additional conditions usually called compatibility equations that involve internal forces or stresses and displacements of points of the structure. There are several general methods that can provide these equations:.

• - matrix method of rigidity.

• - Castigliano's theorems.

• - Mohr's theorems.

• - three moments theorem.

Another important area of ​​machinery design, vibration analysis and seismic design of buildings is dynamic analysis. In this type of analysis, the maximum responses of certain parameters (accelerations, displacements, efforts, etc.) that occur in a structure under dynamic or time-varying loads are sought. That generally requires the use of differential equations. Some common aspects of dynamic analysis include:.

• - modal analysis.

• - determination of own frequencies.

• - determination of resonance phenomena.

Literature

• - Hibbeler, R. C. (2010). Mechanical-static engineering. 12a. ed. Pearson Education, Mexico, 2010. ISBN 978-607-442-561-1.

Node method

The method of the nodes or method of the nodes, consists of the approach of mechanical balance of each of the nodes or knots of a simple reinforcement. A node is each of the points where two or more bars meet. The global balance of the structure implies the local balance of each of the nodes. For the node method to be applicable to a specific structure, some geometric conditions must be met, including:

• - That the structure has articulated nodes or behaves in a similar way to a structure of articulated nodes.

• - That the number of bars is less than a certain amount given by the number of bars:.

Zero force elements

The analysis of trusses by the "node method" is considerably simplified if we can first identify those elements that do not bear load. These zero-force elements are used to increase the stability of the truss during construction and provide additional support if the applied load is modified. Typically, the zero-force elements of a truss can be found by inspection of each of its nodes, making a free-body diagram of the truss and summing the forces. Typically, the zero-force elements are can be determined in the following ways:

• - If only two members form a truss and no extra load or support reaction is applied to the node, the two members must be zero force members.

• - If three elements form a truss node in which two of the elements are collinear, the third element is a zero force element as long as no external force or support reaction is applied to the node.[1]​.

This type of structures cannot be analyzed solely using the statics or equilibrium equations, since the latter provide an insufficient number of equations. Hyperstatic problems require additional conditions usually called compatibility equations that involve internal forces or stresses and displacements of points of the structure. There are several general methods that can provide these equations:.

• - matrix method of rigidity.

• - Castigliano's theorems.

• - Mohr's theorems.

• - three moments theorem.

Another important area of ​​machinery design, vibration analysis and seismic design of buildings is dynamic analysis. In this type of analysis, the maximum responses of certain parameters (accelerations, displacements, efforts, etc.) that occur in a structure under dynamic or time-varying loads are sought. That generally requires the use of differential equations. Some common aspects of dynamic analysis include:.

• - modal analysis.

• - determination of own frequencies.

• - determination of resonance phenomena.

Literature

• - Hibbeler, R. C. (2010). Mechanical-static engineering. 12a. ed. Pearson Education, Mexico, 2010. ISBN 978-607-442-561-1.