Mechanics II Exam 2

Kinematic Assumption

an assumed relationship between position, velocity, and acceleration of a moving object that allows for the prediction of motion based on parameters like time and initial conditions.

Torsion

the twisting of an object due to an applied torque, often resulting in shear stress within the material.

Torque

a twisting couple or rotational force that causes an object to rotate around an axis

Polar Moment of Inertia 

an objects resistance to torsion, or twisting

Torsional Shear Stress

occur on the face perpendicular to the rotation…. internal forces that resist the rotation

Angle of Twist

proportional to the applied torque and shaft length

Power

Torque multiplied by angular velocity (2pi+frequency)

Thin-Walled Member

structural elements that have a wall thickness significantly smaller than their other dimensions, allowing for the assumption of uniform stress distribution across the thin cross-section

Pure Bending

A state of stress within a beam where a constant bending moment is applied, and the shear force is zero.

Area Moment of Inertia

Also known as the Second Moment of Area, it is a geometric property of an area that reflects how its points are distributed with regard to an arbitrary axis. It quantifies a structural member's resistance to bending or deflection and is crucial in beam theory for calculating bending stress and deflection.

Shear Diagram

shows internal shear forces of a beam

Bending Diagram

shows internal bending moments of a beam

Transverse Shear

the internal force and stress that causes layers of a beam to slide past one another when a load is applied perpendicular to the beam's axis (VQ/It)

Cantilever Beam

a rigid structural element fixed at only one end and free at the other, projecting horizontally from its support

Simply Supported Beam

a structural element that is supported at two points, typically near its ends.

Clamped Beam

a beam that is fixed or restrained at both ends, meaning it is rigidly held in place and cannot rotate at its supports.

Bending Stress

the internal stress in a structural element, like a beam, that results from an external bending moment caused by a transverse load. This stress is a combination of tensile stress on one side of the element and compressive stress on the other, with the stress being zero at the neutral axis

Neutral Axis

located at the centroid of the cross-section of a beam.

Transformed Width

The transformed width (or transformed section method) is a technique used in structural mechanics to analyze composite beams made of two or more different materials (e.g., steel and concrete, or wood and steel). This method converts the actual composite cross-section into an equivalent cross-section composed entirely of a single, 'transformed' material. This is achieved by adjusting the width of one material based on the ratio of its modulus of elasticity (Young's modulus) to the modulus of elasticity of the reference material.

Prismatic

In mechanics and materials science, a prismatic member (or beam) refers to a structural element that has a uniform cross-section along its entire length.

Shear Flow

horizontal force/unit length

Area Moment

I about the centroid of a shape times the distance between the centroid of shape that and a desired axis 

Transverse Shear Stress

the stress that occurs in a structural element, like a beam, due to a force applied perpendicular to its long axis. This stress arises from the shear force component of a bending load, causing internal shear stresses within the cross-section that vary from zero at the top and bottom surfaces to a maximum at the neutral axis