Compressing the Femur

Opposite to anxiety forces, compression forces are provided by a product in solution to gift compressed rather than stretched. The resistance of materials to deformation is what causes the normal force (support force) that we introduced in the unit ~ above balance. Because that example, the femur is compressed while sustaining the upper body load of a person.

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The person Femur. Image Credit: Anatomography via Wikimedia Commons

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“In human being anatomy, the femur (thigh bone) is the longest and largest bone. In addition to the temporal bone that the skull, it is among the two strongest skeletal in the body. The average adult male femur is48 cm(18.9 in) in length and2.34 cm(0.92 in) in diameter and also can assistance up to 30 time the weight of an adult.”<2>The median weight among adult males in the United says is 196 lbs(872 N)<3>. According to the statement the the femur deserve to support 30x body weight, the adult masculine femur have the right to support about 6,000 lbs of compressive force! such high forces are rarely generated by the body under its own power, for this reason motor automobile collisions room the number one cause of femur fractures<4>.

Stress

The dimension of object affects exactly how they deform in an answer to applied compression and also tension forces. For example, the best compression or tension pressures that a bone can support depends on the dimension of the bone. Much more specifically, the an ext area available for the pressure to be spread out out over, the an ext force the bone deserve to support. That means the maximum forces bones, (and other objects) can handle space proportional come the cross-sectional area that the bone the is perpendicular (90°) come the direction of the force. Because that example, the force that the femur can support vertically along its size depends ~ above the area of its horizontal cross-sectional area which is roughly circular and somewhat hollow (bone marrow fills the center space).

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These cross sections present the midshaft of the femur of an 84-year-old woman with progressed osteoporosis (right), contrasted to a healthy and balanced femur the a 17-year-old female (left). Picture Credit:Smithsonian nationwide Museum of herbal History

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Larger bones and tendons deserve to support much more force, therefore in bespeak to analyze the behavior of the bone product itself we would must divide the force used to through the cross-sectional area (

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). The resulting quantity is well-known as the anxiety (σ) ~ above the material. Stress has actually units of pressure per area so the SI units are (N/m2) i m sorry are likewise known as Pascals. Devices of pounds per square inch (PSI,lbs/in2) are typical in the U.S.

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Ultimate stamin of the Femur

The maximum stress and anxiety that bone, or any other material, deserve to experience before the material starts fracture or rupture is dubbed the ultimate strength. Notification that product strength is defined in terms of stress, not force, therefore that we are evaluating the material itself, without including the effect of how much material is present. For some materials the ultimate toughness is various when the stress is exhilaration to like the material (compression) versus once the forces are exhilaration to large the product under tension, therefore we frequently refer to can be fried tensile stamin or ultimate compressive strength. For example, the ultimate compressive toughness for human femur bone is measured to it is in 205 MPa(205 Million Pascals) under compression follow me its length. The ultimate tensile strength of femur bone under stress along its length is 135 MPa.<6> together with bone, concrete and chalk space other examples of materials with different compressive and tensile can be fried strengths.


Everyday Example: Femur ultimate Strength

Let’s inspect to watch if the measured worths for compressive ultimate toughness agree v the claim that the person femur can support 30x the adult body weight, or around 6,000lbs

First let’s to convert the declared 6,000 lbs force come Newtons and also work in SI units.

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An almost right minimum cross-sectional area the the femur is

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. (*See the bottom of this example if you room interested in learning how we approximated this value). We divide the compressive pressure by the cross-sectional area to uncover the compressive stress on the bone.

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Our approximate worth for the ultimate toughness of bone that would be required to assistance 30x body load was 80 MPa, i beg your pardon is actually less than the measured value of 205 MPa, therefore the insurance claim that the femur can support 30x body weight seems reasonable.

*This is exactly how we approximated the femur cross-sectional area, skip this if you aren’t interested:

First we divide the 2.34 cm femur diameter quoted earlier by 2 to find the femur radius, climate we transform to typical units of meters.

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Using the equation because that the area that a circle we calculate the full area of the femur come be:

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Finally we have to subtract turn off the area of the hole middle component to obtain the network bone area. We provided a ruler on the above snapshot of the femur cross-sections to view that the within radius is roughly half of the external radius, or

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so us calculate the absent inner area:

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And subtract off the inner area indigenous the total:

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Transverse can be fried Strength

So far we have debated ultimate strengths along the long axis of the femur, recognized as the longitudinal direction. Some materials, such together bone and wood, have various ultimate staminas along various axes. The ultimate compressive strength for bone follow me the short axis (transverse direction) is 131 MPa, or about 36% much less than the 205 MPa longitudinal value. Products that have various properties along different axes are well-known as anisotropic. Materials that act the very same in all directions are dubbed isotropic.

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An amazing fact to finish up this chapter: when a person stands the femur in reality experiences compressiveand tensile emphasize on different sides that the bone. This occurs because the structure of the i know well socket applies the load of the body weight off to the side rather than directly along the long axis of the bone.

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Both tension and compressive stress are applied to the Femur when standing. Image Credit: Blausen medical via Wikimedia Commons

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