The Basic Principles in Structural Mechanics

What are structures in civil engineering? Why is it important to understand? Structures can be defined as shapes or forms such as buildings, bridges, dams, and walls, are designed significantly to resist any applied load (force) without losing its own strength capacities and appreciable deformation. The fundamental purpose of the structure is to transmit all applied loads to the support systems and ultimately through the foundations and to the Earth surface.

Therefore, it is the structural design engineer responsibility to make sure that the required structures to be strong, durable, stable, and safe. A proper process in design stages must be taken and this includes applying mathematical concepts to determine the applied forces and the reactions in the structural elements.

Types of Structures
Structures can be categorized in two types namely frame and mass. The frame structures resist the applied loads by virtue of its geometry, while the mass structures are the type of structures which are able to resist the applied loads by virtue of its weight. The most common structural elements structural elements are arches, beams, columns, foundations, trusses, and walls.

The Basic Structural Elements
The three basic structural elements of the framed structures: Beams, Rods, Slabs (plates). Each of the members is characterized by a dominant form of load-carrying capacity and deformation.

Beams
It defined as slender structural members that can resist bending due to action of applied loads. It is perhaps the most important and widely used structural members and can be classified according to its support conditions. The loads are usually applied normal to the member axis and this will cause a bending action.

Rods
It is essentially subjected to loads along the axis (like axis loads) and the members will be in compression (for a column or strut) or in tension (for tie members) which resultant in deformation under load is a simple change in length.

Slabs or Plates
The members which can sustain loading over a large area with minimal thickness (surface area). The loads can be either applied normal to the plane or along the plane of the slab, and thus have both bending actions and axial forces combined together.

The Structural Forms
Large structures are built significantly to safely withstand large loadings. Thus, to be able to transmit the loads and needed to combine the elementary forms of structural members. For examples, as the span of a beam increases, it becomes uneconomical to use a solid beam. Therefore, it is necessary to introduce frameworks composed of straight members connected at their ends to form rigid structures, such as bridges and roof planes.

Trusses
Trusses provide both practical and economical solutions especially in the design of bridges and buildings. If an entire truss lies in a single plane, it is called a plane truss. Typically, the most simple and stable truss consists of three straight members (triangle shape) connected together at its ends. As for rectangular configuration, be advice that the shape is not suitable for a truss because of instability and shape changes without changing the length of any of the four members, thus swaying will occurred.

Rigid Frames
Another type of structure that is similar to a truss and capable of carrying external loads. The main different is the way that external loads are applied to them. In frames, members maybe applied at any point of any member. The consequence of the difference is that not all frame members are two-forces which as a result may subjected of bending as well. Portal frames and large frames are common types of rigid jointed frames as the joints are stiff, continuous and moment couples occurred.

Arches
Arches are curved structures that are capable of taking bending moments. The basic arch structures are classified as three-pinned and fixed support arch. The forces maybe determined from simple statically analysis, which known as statically determinate for three-pinned. Fixed support arches are statically indeterminate and have to be solved by taking its strain energy into account.

Cabled Structures
It consists primarily of cables, hangers and the main structural component in the form of an arch or girders. The cables normally used to suspend the hangers which resist the weight of the girders, example the bridge.

Types of Joints
All the structural members in framed buildings or trusses must be adequately connected together so that the applied loads are transferred safely to the ground surface. The types of connection or joints are basically divided into two: stiff and pinned joint.

Stiff Joint
This type of joint considered to have fixity at the point of connection and is rigid as it is sometimes called a rigid joint. The feature is that the flexure of one member meets at the joint has an effect on the other members. If it is perfectly stiff, then the angle between the members remains unaltered while rotation takes place.

Pinned Joint
It is sometimes called a hinged joint. As an example, many roof trusses and bridges are constructed using the pinned joint principles. These joints allow relative movement of the members and they cannot resist bending moments, unlike in stiff joints. Nowadays bolting and riveting are more common used, although the members cannot move relatively to one another, at some degree of rotation were allowed in practice. This is due to to the elasticity of the system and deformations of the members are relatively very small as this the common practice of assuming all joints in a truss to be pinned.

Types of Supports
All applied loads on a framed structure will be transferred to the support systems which will then provide the reacting force (reactions) to maintain equilibrium. Some structures are constrained by supports that do not allow any rigid-body movement and other support systems resist translational movement but no resistance to rotation. The behavior of the supports can be a critical effect on the structure proper and therefore cannot be ignored at the design stage.

In the actual practice, it is necessary to make certain idealized simplifications regarding the nature of supports. The common types of support are fixed or built-in, pinned and rollers support.

The Determinacy Conditions
To be in a state of static equilibrium, a structure must meet the requirements of stability. Structural stability can be accomplished through the geometry of the members and the support conditions present. The structures that are statically indeterminate can be classified either as externally or internally determinate depending upon the unknown forces. An internally statically indeterminate structure is the one that has redundant or extra members within the structures (in frames or trusses).

Beams
In simple beams, the condition for determinacy is that the support must be such that there are not more than three reactive forces. In a beam which is built-in (fixed) at one end and simply supported (or propped) at the other end, this is known as statically indeterminate.

Trusses
A stable (simple) truss which is classified as statically determinate. If two members are added to the truss to form another triangle, then one more joint has been added. Then, this mean the truss will remain perfectly stable if this relationship is satisfied.

Therefore, 2j = m + 3
where j = number of joints, and m = number of members.

Determinate trusses can be determine by: Joints method, Sections method or graphical method. As for indeterminate trusses, solving methods usually require solutions of simultaneous equations or by linear techniques.

Frames
Frames are also classified as statically determinate or indeterminate which depends upon the internal forces within the members or external reactions.For a plane frame if each member represents three unknown forces, then the total number of unknowns is equal to the sum of the number of unknown reaction components (r) and the unknown forces.

Therefore, 3j = 3m + r
where j = number of joints, m = number of members, and r = number of reactions.

Determinacy for structures can be categorizes as statically determinate (just-stiff) and statically indeterminate (over-stiff), particularly in trusses and frames.

In conclusion, these are the basic principles in structural mechanics before proceed to further in this subject. These principles are the introductory understanding of arches, beams, cables, frames, trusses, and so forth.

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