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Bend allowance

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

Descartes' theorem ( internally tangent circle to three given kissing circles)

n geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic ... more

Knuckle joint (Maximum bending stress)

A knuckle joint is a mechanical joint used to connect two rods which are under a tensile load, when there is a requirement of small amount of flexibility, ... more

Bending Stress

In Applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied ... more

Bending moments at any point along the span of a cantilevered beam with the free end supported on a roller

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Maximum value of bending moments for a center loaded beam supported by two simple supports

A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. ... more

Bending moments at any point along the span of a uniformly loaded cantilevered beam

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Maximum value of bending moments for a cantilever beam with uniformly distributed load

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Maximum value of bending moments for a cantilever beam with end load

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Shaft bending moment due to yaw (2-bladed rotor)

The shaft bending moment due to yaw depends on the blades of the rotor. In this case the rotor has 2 blades

... more

Wind turbine yaw error

All wind turbines operate with a yaw error. In this case an extreme yaw error of 30 degrees is assumed. The flapwise blade root bending moment due to that ... more

Blade root bending moment load due to yaw

The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more

Velocity of the reciprocating motion of the piston with respect to crank angle

A piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from ... more

Mohr–Coulomb failure criterion

Mohr–Coulomb theory is a mathematical model describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as ... more

Moment of Inertia - Sphere (hollow)

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Moment of Inertia - Sphere (solid)

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Second moment of area - I-Beam (W-section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

Moment of Inertia - Right Circular Cone - z axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Moment of Inertia - I-Beam (Ideal cross section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

Moment of Inertia - Sphere (solid) - y axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Precession - (Torque-induced - Classical Newtonian)

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Moment of Inertia - Right Circular Cone - x and y axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Moment of Inertia - Sphere (shell)

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Solar Rotation

Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator ... more

Knuckle joint (Moment about axis XX)

A knuckle joint is a mechanical joint used to connect two rods which are under a tensile load, when there is a requirement of small amount of flexibility, ... more

Kepler's Second Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Rotary variable differential transformer(RVDT) - Rotor mechanical angle

A rotary variable differential transformer (RVDT) is a type of electrical transformer used for measuring angular ... more

Curvature of a Bimetallic Beam

A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... more

Worksheet 316

Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 45.0 cm long and 2.00 cm in radius.

Strategy

The force is equal to the weight supported:

Force (Newton's second law)

and the cross-sectional area of the upper leg bone(femur) is:

Disk area

To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be 9×109 N/m2. Now,all quantities except ΔL are known. Thus:

Young's Modulus

Discussion

This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(see reference below) have larger values of Young’s modulus Y . In other words, they are more rigid.

Reference:
This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

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