Structural Engineering

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What is Structural Engineering?

Structural engineering is a branch of engineering which deals with the analysis and design of various structural systems. Although this branch of engineering has influence on various other disciplines like mechanical or aeronautical engineering, etc it is more commonly identified with civil engineering.structural engineering deals about the conception, design, and construction of the structural systems that are needed in support of human civil engineering

Structural Engineering Activities

Structural engineering is mainly involved with two activities

1. Structural Analysis

2. Structural Design

Structural Analysis

It deals with analysing a particular structural system. A structural system may vary from simple systems (like beams, columns, slabs, etc) to more complex systems (like frames, bridges, piers, foundations, retaining walls, etc). The objective behind analysis is to estimate or find resultant stresses (or forces) so that these elements can be designed to withstand the load that comes over it.

Analysis of Statically Determinate Structures

Idealized Structures

In reality the exact analysis of a structure can never be carried out. Idealizing a structure is a method of conservatively simplifying the components of the structural system, while keeping its behavior under loading the same. This is done in order to simplify calculations. Without an idealized structure, design could take a massively longer amount of time... and sometimes becomes impossible. It is important for a structual engineer to develop methods to idealize a structure in order to carry out analysis.

Supports for Coplanar Structures

Structural Members are joined together by supports depending on the intent of the engineer. Three types of joints most often used are pin connections, roller supports, and fixed joints. Pin connections provide vertical and lateral support, but cannot provide a moment reaction. A roller support can only supply a reaction of a force in one direction. A fixed joint provides vertical, lateral as well as a moment reaction.

Analysis of Statically Determinate Trusses

Typically done using method of joints, or method of sections.

Internal Loadings Developed in Structural Members

Internal loadings are found by "cutting" the member and applying the equations of equilibrium.

Influence Lines for Statically Determinate Structues

Influence lines are a diagram that represents variation of a loading function at one location on a structure. For example, a truck drives across a bridge:

When the truck is at the left side on top of the bridge, very little loading is felt at the right support. The function represented by influence lines changes as the truck moves towards the right end of the bridge. The loading at the right support grows as the truck nears it, until the truck reaches the far end, where the end realizes the maximum loading. Influence lines for statically determinate structures consist of a straight line.

Deflections

Deflections occur naturally in structures from various sources. Loads and temperature changes are sources of deflections that structural engineers have to design for because they are unavoidable. Designs must be made in order to avoid cracking of the materials used. Fabrication or Design Errors can lead to failure of structures and should be avoided through careful planning and analysis.

Structures in most cases are built with materials that can withstand the designed loading and only have a linear elastic response. Under these conditions loads may cause deflections, but when the load is removed the structure will return to it original shape and strength. Overloading beyond the linear elastic response may cause damage and failure of the structure. This is referred to as "plastic deformation".

Elastic-Beam Theory

If a material is homogeneous and behaves in a linear elastic manner we can derive a nonlinear second order differential equation that when solved through the double integration method can give a solution deflection as a function of x. We must assume $dv/dx=0$ relative to the length of the beam in the x-axial direction.

$\frac{d^{2}v}{d{x}^2}=\frac{M}{EI}$

M = the internal moment in the beam E = the material's modulus of elasticity I = the beam's moment of inertia computed about the neutral axis v = deflection

The Double Integration Method

When Moment can be expressed as a function of position x, then performing double integration will yield the beam's slope as a function of x, and the equation of the elastic curve.

The two integrations will yield two constants of intergration. Using the boundary conditions the constants can be solved for.

Castagliano's theorems

First theorem

If the strain energy of an elastic structure can be expressed as a function of generalised displacement qi; then the partial derivative of the strain energy with respect to generalised displacement gives the generalised force Qi.

Using this theorem the generalised forces acting on the structure can be calculated.

Second theorem

If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Qi; then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement qi in the direction of Qi.

Using this theorem the generalised displacement of the structure can be calculated. Castigliano's method usually refers to the application of his second theorem.

Structural Design

Structural design is the process of selecting members of required dimensions such that they provide adequate stability under service loads. There are two conditions that a structural designer must keep in mind. One is "stability" and the other is "serviceability". Stability of a structure means that it can resist the loads acting on it satisfactorily and that the structure will not collapse immediately (that is, it provides enough time to escape to safety). Serviceability refers to certain conditions that are required so that the structure remains serviceable. For example, consider a bridge that can resist service loads without collapse. This is a "stable" structure. Now assume that this bridge shows abnormal deflections. The deflections could be such that the bridge feels bouncy and could lead to steering problems for vehicles crossing it at high speeds. As such this may not cause the structure to collapse. So we can say that the structure is stable, but according to serviceability criterion it is not serviceable because people could feel afraid of using the bridge.

In the design and construction of the foundation and framing for buildings and bridges, the main materials used are concrete, steel, timber, and masonry. Steel can further be subdivided into two subsections: hot-rolled steel and and cold-formed steel. Cold-formed steel applies to material of approximately 1/8" or less in thickness that is either folded or roll-formed from flat sheets into structural shapes while at room temperature.

Safety Factors

All structures must be designed to carry all foreseeable loads with a suitable factor of safety. Clearly it would be unsafe to walk on a structure that was adequate but had no margin of safety built in. With this in mind, most countries have standards that prescribe the required minimum safety factors for structures. The minimum is usually a factor of about 1.7. This is not a factor to allow for overloading or poor workmanship. If there is a possibility of overloading or poor workmanship, the design loads must be increased to account for the overloading and the strengths of the materials upon which the design is based must be reduced to account for the poor workmanship. The safety factor must remain complete, as it is there to account for the unexpected events and unforeseen circumstances. If a structure becomes worn, loose, cracked or corroded, it should always be repaired so the safety factor is preserved.