Fundamentals of Material Resistance and Structural Mechanics

Material Resistance and Stiffness

Resistance is the property that support materials have against the action of forces, while material stiffness is the ability to resist deformation.

Types of Loads

• Static: Applied gradually from zero to maximum.
• Dynamic Load: Applied at a certain speed on the body that must endure it. It is divided into sudden load, shock-free, and forced shock.
• Sudden Load: Applies its maximum value instantly.

Mechanical Efforts

• Effort: An internal force that originates from a resistive element and is transmitted through a flat section of it.
• Tensile Strength: Stress perpendicular to the cross-section of the body that tends to elongate the fibers.
• Compression Effort: A negative voltage, since the load tends to shorten the fibers of the piece.
• Bending Stress: Acts on a body, tending to bend it while stretching and cutting other fibers.
• Shear Force: Contained in the section and tends to cut the piece by sliding the affected sections.
• Torsion Effort: Occurs when forces tend to twist the pieces on their axis.
• Compound Effort: A combination of several efforts acting on the solids.
• Buckling Effort: A combined effort of bending and compression.
• Voltage: The effort per unit area.

Hooke's Law

Hooke's Law relates the forces acting on a solid with the strain produced, indicating proportionality; i.e., double the charge results in double the deformation. The maximum voltage that determines the boundary of the application of Hooke's law is the limit of proportionality.

Rules for Drawing Diagrams

• Calculate beam reactions.
• Section the beam and analyze the sections of constant load.
• Determine the efforts of those sections.
• In a section with a concentrated load, there will be a jump in the shear diagram.
• In a section with a concentrated load, there will be a change of slope in the bending moment diagram.
• When the shear stress is 0, the bending moment is at its maximum.
• Draw the shear stress diagram before drawing the bending moment diagram.

Types of Bending and Stress Analysis

• Pure Bending: In any section of the piece, only a bending moment exists.
• Simple Flexure: In any section of the piece, there is a bending moment and shear.
• Composite Flexure: In any section of the piece, there is a bending moment, shear, and normal stress.

Stress-Strain Tensile Test Diagram

On a steel cylinder, a gradually increasing tractive effort is applied, starting from zero, representing the strains and tensions that arise:

• Limit of Proportionality: The period of elongation proportional to the loads.
• Limit of Elasticity: Point E is the elastic limit. The OE zone is elastic because when charging stops, the specimen returns to its normal state, but when E is exceeded, permanent deformation occurs.
• Limit of Influence: The section EF is slightly curved, indicating the beginning of the plastic zone.