Structural Analysis: Design, Forces, and Stability
Link: the condition imposed on an item about to stand still or describing its trajectory. The way to realize the support links is cn.
Structure: This refers to something that is built. These consist of one or more resistance elements arranged so that both the overall structure and its components are able to remain without significant changes in geometry during loading and unloading.
Structural Design is aimed at two main objectives: 1) Meeting the requirements of functionality; 2) Safely carrying the loads.
The complete design of a structure is established as follows: 1) Identification of the general form; 2) Investigation of loads (dead-load, stress, impact load, dynamic loads); 3) Analysis of stress; 4) Selection of the various elements; 5) Drawings and details.
Beams: Are straight elements subjected only to transverse loads; analyzes bending element values.
Trusses: Different types of trusses exist depending on the required structural solution. Its construction is done by uniting straight elements at a few points called nodes, forming a geometry such that the system behaves stably when receiving loads applied directly to these nodes.
Lattice: It is a lattice of straight bars interconnected in flat triangles forming knots. The interest of this type of structure is that the work is predominantly in bar tension (frames).
Real Geometry: Is a set of characters used to represent a three-dimensional geometric space on a two-dimensional surface and to solve problems in two spatial dimensions of the process, ensuring, through reversibility, the proper reading.
Mark: A frame that serves as support to other elements.
Truss Basics: The fundamental principle is to attach straight elements to form triangles. This allows for carrying transverse loads between two supports using less material than a beam, but with the disadvantage that the elements occupy a substantial vertical height.
The union between two points can be made with an arch formed by two inclined linear elements in compression (Fig. A) restricted by two supports pushing to prevent opening. The horizontal thrust may be replaced by a tension element connecting two released inclined elements to support the outward thrust (Fig. B). The load can also be carried with two tension elements and a horizontal compression element (Fig. C).
Hyperstability Grades: No restriction is redundant; minimal restrictions are needed to reach the static equilibrium of a structure, whether a base, a structure, or a lattice. There are two equations of formulas: (GH = No restrictions – n of Eq. in balance) (RI = n of restraints – No. of nodes x 2 – n eq. equilibrium).
Retaining Walls: A structure of rigid material designed to contain earth.
- Gravity walls: These walls counteract the weight of the ground thrust.
- Reinforced concrete and earth walls: These use metal skeletons to resist movement.
- Structural concrete walls: These are heavily reinforced.
Check in calculating typical embankment: Checkout: Bonded; dump; of carrying capacity; global stability.
Strength: Every agent is able to change the speed or shape of objects. It is a vector quantity capable of deforming bodies or modifying their velocity, overcoming their inertia and moving them if they were mobile (static and dynamic effects).
Torque: A system of two equal, parallel, and opposite forces. Applying a torque to a body produces a shift or rotation. This shift depends on the value of the forces forming the pair, their sense, and the distance between them (torque arm).
Parallel Forces: If two or more forces act on a rigid body with parallel lines of action, the resultant will have a value equal to the sum of the forces. Its line of action must be accurately determined to minimize the effect as components.
Concurrent Forces: A system for which there is a common point for all the lines of action of the component forces. The resultant is the simplest element to which the system of forces can be reduced.
Non-Concurrent Forces: A group of forces acting on the same body whose lines of action do not intersect at the same point.
Fundamental Forces: Forces of the universe that cannot be explained in terms of other more basic forces. There are four fundamental forces:
- Gravity: The force of attraction exerted on one mass by another, affecting all bodies.
- Electromagnetic: Affects electrically charged bodies.
- Strong Nuclear: Holds the constituents of atomic nuclei together.
- Weak Nuclear: Responsible for the decay of neutrons.
Force Polygon: The algebraic sum of the projections of the given forces on any pair of orthogonal axes must be zero.
Force Polygon Method: The resultant force of two or more forces can be calculated using the force polygon method as follows: 1) Place one force below the other, forming a polygon; 2) Connect the origin of the first force to the endpoint of the last; 3) This last vector is the resultant of the system.
Coplanar Force System: A force is an action of one body on another and is characterized by magnitude, direction, and sense of application.
- Magnitude: The magnitude of the force related to its units.
- Direction: The orientation of its line of action.
- Sense: Indicates the direction of the force.
- Application Point: Its position.
Coplanar forces are in the same plane and have two axes, unlike forces that are coplanar in more than one plane (i.e., in three axes).
Varignon’s Theorem: The moment about a given point of the resultant of concurrent forces is equal to the sum of the moments of each of the forces about the same point.