1.1. Structural Concepts

Structural Concepts

• Rigid body: A body whose parts are fixed relative to each other, simplifying analysis.
• Force: Causes a change in the body's state of motion; characterized by magnitude, line of action, and direction.
• Force system: Arrangement of forces acting on a body, classified as coplanar or non-coplanar.
• Types of force systems: Concurrent (lines of action intersect), parallel (lines of action are parallel).
• Principle of transmissibility: External effect of a force is constant regardless of application point along its line of action, but internal effects are dependent on the point of application.

Principles of Static Equilibrium

• Static Equilibrium: A body with balanced forces is at rest.
• Free body diagram: A sketch displaying forces exerted on a body, helping analyze equilibrium.
• Strength of materials: Studies the relationship between external loads and their internal effects on bodies.
• Types of external loads: Axial, twisting (torque), bending loads, and combinations.

Stress-Strain Relationships

• Stress: Force per unit area (S = P/A).
• Strain: Unit deformation.
• Proportional limit: The point where stress is directly proportional to strain (Hooke's Law).
• Elastic limit: Stress beyond which the material doesn't return to its original shape when unloaded.
• Yield point: Significant elongation without increased load, used for steel design.
• Yield Strength: For materials lacking a defined yield point, it's determined by the offset method.
• Ultimate stress/strength: Highest stress value the material can withstand.
• Rupture strength: Stress at failure (lower than ultimate in structural steel).
• Allowable stress: Limited to values below the proportional limit, often based on yield or ultimate strength divided by a factor of safety.

Types of Failure in Beams

• Flexural failure: Occurs when the load exceeds the beam's flexural capacity.
• Shear failure: Results from insufficient shear resistance between beam materials.

Bending and Buckling

• Bending: Caused by a transverse load perpendicular to the neutral axis, creating bending stress.
• Buckling: A sudden change in shape under axial load, occurring due to increasing axial load.

Hooke's Law - Axial Deformation and Modulus of Elasticity

• Modulus of elasticity: Measures a material's resistance to elastic deformation.
• Hooke's law: Describes the relationship between stress and strain in a material.

Structural Loadings

• Prevailing Design Load: Considers axial load, material overstressing, and buckling.
• Dead loads: Weight of the structure and permanently attached items.
• Minimum Design Dead Loads: Includes values for ceilings, acoustical boards, gypsum boards, coverings, insulation, floor finishes (e.g., cement, tile, terrazzo, wood).
• Movable loads: Loads that can be moved, often applied gradually (e.g., storage contents).
• Live loads: Loads varying in position, classified as movable and moving loads.
• Impact: Increase in stress due to rapid application of a load.
• Snow and ice loads: Considered movable, as they don't always cover the entire roof.
• Minimum Uniform Live Loads: Vary for different building types (e.g., hospitals, offices, schools).
• Minimum Roof Live Loads: Depend on roof slope.

Lateral Loads

• Wind loads: Important for large structures with open interiors.
• Soil pressure: Active pressure is about half of vertical pressure, while passive pressure is about four times the vertical pressure.
• Hydrostatic pressure: Loads on dams, tanks, calculated using hydraulic principles.
• Earthquake forces: Structures must be designed to withstand earthquake effects, especially horizontal accelerations.
• Centrifugal forces: Act on curved bridges, treated as moving loads.
• Longitudinal forces: Horizontal forces acting along the roadway (e.g., forces on a bridge).

Structural Forms

• Steel-cable structure: Efficient for carrying loads through tension.
• Flexible membrane: Carries loads by tension, similar to many cables side-by-side.
• Arch: Inverted cable structure, conforming to the equilibrium polygon based on the load.
• Shell: Membrane with flexural stiffness and strength (like an arched cable), often made of reinforced concrete.
• Planar truss or planar framework: Supports concentrated load with a two-member arch.
• Space framework: Supports three-dimensional structures, using a tetrahedral nucleus.
• Framed structure: Beams can be cantilevered or end-supported, commonly used in modern construction.