The Basic Principles in Structural Mechanics

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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, designed significantly to resist any applied load (force) without losing their 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's surface.

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

Types of Structures

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

The Types of Structures

The Basic Structural Elements

The three essential structural elements of the framed structures are beams, Rods, and Slabs (plates). Each member is characterised by a dominant form of load-carrying capacity and deformation.

Beams

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

Rods

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

The Forces in Members

The Structural Forms

Large structures are built significantly to safely withstand large loadings. Thus, to transmit the loads and combine the elementary forms of structural members, to be able to transmit the loads. For example, as the span of a beam increases, it becomes uneconomical to use a solid shaft. 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, primarily 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 (triangular shape) connected at its ends. As for rectangular configuration, be advised 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 occur.

Rigid Frames

Another type of structure is similar to a truss and capable of carrying external loads. The main difference is the way that external loads are applied to them. In frames, members may be 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 to 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 archs. The forces may be determined from simple static analysis, which is known as statically determinate for three-pinned. Fixed support arches are statically indeterminate and have to be solved by taking their 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.

The Structural Forms

Types of Joints

All structural members in framed buildings or trusses must be adequately connected to transfer the applied loads to the ground surface. The types of connection or joints are basically divided into two: stiff and pinned joints.

Stiff Joint

This type of joint is 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 affects the other members. If it is perfectly stiff, the angle between the members remains unaltered while rotation occurs.

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.

The Types of Joints

Types of Supports

All applied loads on a framed structure will be transferred to the support systems, providing 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 behaviour of the supports can be a critical effect on the structure proper and, therefore, cannot be ignored at the design stage.

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

The Types of Support

The Determinacy Conditions

A structure must meet the stability requirements to be in a state of static equilibrium. Structural stability can be accomplished through the geometry of the members and the support conditions present. The statically indeterminate structures can be classified either as externally or internally determinate depending upon the unknown forces. An internally statically indeterminate structure 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 shaft 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 means 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 determined by the joints, Sections, or graphical methods. As for indeterminate trusses, solving methods usually require solutions of simultaneous equations or linear techniques.

Frames

Frames are also classified as statically determinate or indeterminate, depending on the members' internal forces 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.

The Determinacy Conditions

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 of structural mechanics before proceeding further in this subject. These principles are the introductory understanding of arches, beams, cables, frames, trusses, etc.