Introduction to Structural Theory

Structural analysis is the prediction of the performance of a given structure under prescribed loads and/or other external e¤ects, such as support movements and temperature changes. The performance characteristics commonly of interest in the design of structures are (1) stresses or stress resultants, such as axial forces, shear forces, and bending moments; (2) deflections; and (3) support reactions. Thus, the analysis of a structure usually involves determination of these quantities as caused by a given loading condition.

WHAT ARE STRUCTURAL FORMS?

The combination of structural elements and the materials from which they are composed is referred to as a structural forms. They are used to support both dead and live loads and to contain/protect things. A structural system can be subdivided into three basic types: Mass structures, Frame structures, and shell structures.
Mass structures is comprised of materials combined together to form a solid structure. The strength of a structure depends on the weight and hardness of a material used. Examples of a mass structure are mountains, brickwalls, pyramids, dams, barriers, etc.
Frame structures are made up of struts combined to form a structural framework. Its structural strength heavily relies on the elements and connections such as joints, and the way the structure is organized. Examples of frame structures include houses, bicycles, and skeletons.
Shell structures are closed-form structures made up of thin material. It has a curved outer membrane that is used as a roof cover in buildings. The structure can maintain its form and are capable of maintaining shape or supporting loads without using frame or solid mass materials.

NATURE OF LOADS

CONCENTRATED LOAD

These are the loads which only acts on a point of a structural member.

UNIFORMLY DISTRIBUTED LOAD

It is a force that is applied evenly over the distance of a support. For the least amount of deflection possible, this load is distributed over the entire length of the support.

UNIFORMLY VARYING LOAD

Uniformly Varying Load (UVL) A UVL is one which is spread over the beam in such a manner that rate of loading varies from each point along the beam, in which load is zero at one end and increase uniformly to the other end.

WHAT IS A BUILDING MATERIAL?

Building materials refer to any materials that can be used for construction purposes. These commonly include woods, clay, rocks, steel, cement, metal, etc. Building materials range from naturally occurring substances to man-made products, and are widely known due to its segmentation into other specialty trades such as carpentry, tiling, insulation, plumbing, and roofing work. All building materials are used to construct a quality structure. Thus, these materials have greatly improved over decades, providing specific benefits and additional structural integrity in the building.

SUPPORTS, REACTIONS, INDETERMINANCY, DEGREES OF FREEDOM, INSTABILITY, STABILITY AND REDUNDANCY OF STRUCTURES

SUPPORTS

Structural support is one of the integral parts of a structure, for it specifies how forces are transferred to the ground from the structure.It provides the necessary stiffness and strength in order to withstand internal forces and guide them safely to the ground. It can be located at the end or at any intermediate point of a structural member that can be either welded or bolted connections, connected by nails, bolts, glue, or engineered connectors.

REACTIONS

The reactions exerted in a two-dimensional structure can be categorized into three types which corresponds depending on types of supports and connections present in a structural element.

a. Reactions equivalent to force with a known line of action - Supports and connections causing reactions of this type include rollers, rockers, frictionless surfaces, short links and cables, collars on frictionless rods, and frictionless pins in slots. These type of supports and connnections can prevent motion in one direction.

b. Reactions Equivalent to a Force of Unknown Direction and Magnitude – Supports and connections resulting to such type of reactions includ frictionless pins in fitted holes, hinges, and rough surfaces. They prevent translation of the free body in all directions, but allows the body from rotating about the connection.

c.Reactions Equivalent to a Force and a Couple - These reactions are caused by fixed supports that oppose both two components of a force and a moment, constraining the support completely.

DEGREES OF FREEDOM

When a structure is loaded, specified points on it, called nodes, will undergo unknown displacements. These displacements are referred to as the degrees of freedom for the structure, and in the displacement method of analysis it is important to specify these degrees of freedom since they become the unknowns when the method is applied.

determinate and indeterminate structure

A structure can be considered as statically determinate when all the unknown reactions or internal members can be determined strictly using equilibrium conditions. On the other hand, a structure can be referred to as statically indeterminate if they have more unknown forces than the available equilibrium conditions. Additional equations, also known as compatibility equations are needed to solve for these unknown reactions.
They are obtained by relating the applied loads/reactions to the displacement or slope on different points of the structure. It involves analysis of geometric and physical properties of structure in order to solve these unknown forces.

BEAMS, TRUSSES, CABLES AND ARCHES, PLANE FRAMES AND INFLUENCE LINES

WHAT IS A BEAM?

A beam is a horizontal structural member that resist the lateral and transverse loads applied to the beam’s axis. It can be made up of steel, wood, and aluminum and can be referred as structural members, elements, rafters, shafts, or purlins. Beams are primarily designed to resist bending moment; however, if they are short and carry large loads, the internal shear force may become quite large and this force may govern their design. Beams can be connected with the column (direct support) or with another beam (indirect support).

cables and arches

Arches and Cables are structures used to span long distances. Cables are usually flexible and carry their loads in tension. They are commonly used to support suspension bridges, transmission lines, and building roofs. It has the ability to take different shapes when subjected to different types of loadings. Cables take the shape of a curve under uniform load, and takes the form of linear segments between load points of application when it is subjected to concentrated load. Since they are subjected to tension, cables will not become unstable and suddenly collapse, as may happen with beams or trusses. Furthermore, the truss will require added costs for construction and increased depth as the span increases. Use of cables, on the other hand, is limited only by their sag, weight, and methods of anchorage.

frames

Plane frames are two-dimensional structures used in construction of buildings and are composed of beams and columns that are either pin or fixed connected. The elements of plane frame are subjected to axial forces, shear and bending moments similar to truss members and beams respectively. The strength of such a frame is derived from the moment interactions between the beams and the columns at the rigid joints. Its elements are usually fixed-connected or semi-fixed depending on the amount of rotational restraint designed into the connection.

INFLUENCE LINE

An influence line represents the variation of either the reaction, shear, or moment, at a specific point in a member as a concentrated force moves over the member. Influence lines can be defined as a graph whose ordinates show the variation of the magnitude of a certain response function of a structure as a unit load traverses across the structure. Influence lines represent the effect of a moving load only at a specified point on a member, whereas shear and moment diagrams represent the effect of fixed loads at all points along the axis of the member.

CLASSWORK ASSIGNMENT #1-#3

Classwork Assignment 1 Module 1_BARTOLOME (1).pdf

Classwork Assignment 2 Module 1_BARTOLOME (1).pdf

Classwork Assignment 3 Module 1_BARTOLOME (2) (1).pdf

Classwork Assignment 4 Module 1_BARTOLOME (1).pdf

COURSEWORK #1

BARTOLOME_COURSEWORK 1 (CENG121) (1).pdf

REFLECTION:

Structural Theory is a general subject that gives the principles and laws that govern how loads affect structures in general. The theory of structures is concerned with establishing an understanding of the behaviour of structures such as beams, columns, frames, and plates when subjected to applied loads or other actions which have the effect of changing the state of stress and deformation of the structure. In addition, structural design is the application of structural theory to ensure that buildings and other structures are built to support all loads and resist all constraining forces that may be reasonably expected to be imposed on them during their expected service life, without hazard to occupants or users and preferably without dangerous deformations, excessive sideways or annoying vibrations. Theory of structures helps us to understand how our spaces can be brought to life. We have to know if the spaces need to be arranged differently from what was planned. We have to know of the design is actually feasible. For these, we need to know how structural elements behave when subjected to load conditions.

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