Structural Engineering: Statically Indeterminate Beams

Structural Analysis and Loads

• Introduction to structural analysis involves understanding the principles and methods for calculating stress, shear, bending moment, and deflection of structural members.
• Loads on structures include dead loads (permanent loads like walls, floors), live loads (movable loads like people, furniture), and environmental loads (wind, snow, rain).

Analysis of Statically Determinate Beams

• Statically determinate beams involve calculating reactions and internal forces using equilibrium equations.
• Equilibrium and support reactions are crucial concepts for analyzing statically determinate beams.

Determinacy and Stability of Structures

• A structure is considered internally stable if its shape remains unchanged when detached from its supports.
• Internally unstable structures deform when detached, often collapsing under their own weight.
• Stability is essential for structural integrity.
• Statically determinate structures require a minimal number of support reactions to limit deformation.
• Statically indeterminate structures need an excess number of support reactions than required for equilibrium, adding complexity when calculating reactions.

Engineering Structures

• Engineering structures are composed of one or more solid elements, including bridges, buildings, walls, dams, towers, and shells.
• The design process necessitates considerations regarding performance requirements and load-carrying capacity.
• The typical stages for designing a structure include developing a general layout, investigating loads, stress analysis, selecting materials or elements, and creating detailed drawings.
• Beams are straight members subjected to transverse loads. Different types exist depending on how they are supported, for example, cantilever, simply supported, overhanging, continuous, and fixed ended.
• Trusses are structures composed of members connected by frictionless hinges or pins. Various types of trusses include King Post, Queen Post, Howe, Fink and more.
• Rigid frames comprise members connected by rigid joints, capable of resisting moments.

Load Calculations

• Dead loads incorporate the weight of the structure (walls, floors, roof and permanent material).
• Live loads refer to movable or temporary loads (people furniture, equipment).
• Impact loads encompass dynamic forces acting over short periods (moving vehicles, machinery, dropping weights).
• Environmental loads involve external factors like rain (water accumulation), wind (pressures influenced by wind flow), snow (accumulated mass on the roof), and seismic loads (ground movement). Hydrostatic pressure accounts for water exerting pressure on surfaces and earth pressure deals with soil pressure.

Equations of Equilibrium

• Equilibrium equations are mathematical expressions which describe the balance of forces and moments within a structure.
• ΣFx = 0 (sum of horizontal forces equals zero)
• ΣFy = 0 (sum of vertical forces equals zero)
• ΣMa = 0 (sum of moments equals zero)

Types of Supports for Plane Structures

• Link support: the reaction acts in the direction of link or cable.
• Smooth pin or hinged support: reaction is composed of vertical and horizontal components.
• Roller support: reaction is perpendicular to the surface.
• Slider support: reaction involves both an axial force and a moment.
• Fixed connected collar support: reaction involves both an axial force and a moment.
• Fixed support: reaction involves horizontal and vertical components as well as a moment.
• Smooth pin-connected collar support: reaction acts perpendicular to the surface.
• Smooth contact surface: reaction also acts perpendicular to the surface.

Loading Idealization

• Concentrated or point loads act on a small elemental area.
• Distributed loads affect areas or volumes over lengths, areas, or volumes.
• Uniformly distributed loads remain consistent across the area, whereas linearly distributed loads vary in intensity across the area.

Equivalent Concentrated Loads (ECL)

• Equivalent concentrated loads convert distributed or other load types into a single concentrated load.

Inclined Loading

• Inclined loads are at an angle or slope ratio.
• Trigonometry is typically used when analyzing.
• Break inclined loads into x and y components.

Stability and Determinacy of Structures

• Stability examines the ability of a structure to maintain its shape and not deform under loads.
• Determinacy assesses if equilibrium equations suffice to determine support reactions of a structure.
• Internally stable structures maintain their shape when unloaded. Nonrigid structures are prone to deformation.
• Statically determinate structures have sufficient equilibrium equations equal to the unknown support reactions.
• Statically indeterminate structures have more reactions than possible from equilibrium equations requiring additional information.
• Geometric instability is also an issue for stability.
• Degree of indeterminacy reflects support reactions or rigid components exceeding those necessary for maintaining equilibrium.