Compressing the Femur

Opposite to stress forces, compression forces are listed by a product in solution to being compressed fairly than stretched. The resistance of materials to deformation is what causes the normal force (support force) that we presented in the unit ~ above balance. Because that example, the femur is compressed while supporting the upper body load of a person.

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The human being Femur. Picture Credit: Anatomography via Wikimedia Commons


“In person anatomy, the femur (thigh bone) is the longest and largest bone. Together with the temporal bone of the skull, it is one of the 2 strongest bones in the body. The typical adult male femur is48 cm(18.9 in) in length and2.34 cm(0.92 in) in diameter and also can support up to 30 time the weight of an adult.”<2>The mean weight amongst adult males in the United says is 196 lbs(872 N)<3>. Follow to the statement that the femur have the right to support 30x human body weight, the adult masculine femur have the right to support roughly 6,000 lbs of compressive force! together high pressures are rarely created by the human body under its own power, for this reason motor car collisions space the number one cause of femur fractures<4>.


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

These overcome sections display the midshaft that the femur of one 84-year-old mrs with progressed osteoporosis (right), contrasted to a healthy femur that a 17-year-old mrs (left). Photo Credit:Smithsonian national Museum of herbal History


Larger bones and tendons can support an ext force, therefore in bespeak to analyze the actions of the bone material itself we would need to divide the force applied to by the cross-sectional area (

). The resulting quantity is known as the anxiety (σ) top top the material. Stress has actually units of pressure per area for this reason the SI units space (N/m2) i m sorry are likewise known as Pascals. Systems of pounds every square customs (PSI,lbs/in2) are typical in the U.S.



Ultimate toughness of the Femur

The maximum anxiety that bone, or any kind of other material, have the right to experience before the material starts fracture or rupture is called the ultimate strength. Notification that material strength is identified in terms of stress, no force, therefore that we are evaluating the material itself, without including the impact of how much material is present. For some materials the ultimate strength is various when the anxiety is acting to to like the material (compression) versus once the forces are exhilaration to big the material under tension, therefore we frequently refer to ultimate tensile stamin or ultimate compressive strength. Because that example, the can be fried compressive stamin for human femur bone is measured to it is in 205 MPa(205 Million Pascals) under compression along its length. The ultimate tensile strength of femur bone under stress along its length is 135 MPa.<6> together with bone, concrete and also chalk are other instances of materials with various compressive and also tensile can be fried strengths.

Everyday Example: Femur ultimate Strength

Let’s inspect to see if the measured worths for compressive ultimate stamin agree through the claim that the person femur deserve to support 30x the adult body weight, or roughly 6,000lbs

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


An approximate minimum cross-sectional area that the femur is

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


Our approximate worth for the ultimate strength of bone that would certainly be forced to support 30x body weight was 80 MPa, i m sorry is actually less than the measured value of 205 MPa, for this reason the claim that the femur can support 30x body weight appears reasonable.

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

First we division the 2.34 cm femur diameter quoted previously by 2 to discover the femur radius, climate we transform to standard units of meters.


Using the equation for the area of a circle we calculate the complete area that the femur to be:


Finally we have to subtract turn off the area that the hole middle part to acquire the network bone area. We supplied a leader on the above snapshot of the femur cross-sections to watch that the inside radius is roughly fifty percent of the external radius, or

so us calculate the missing inner area:


And subtract off the inside area from the total:


Transverse ultimate Strength

So much we have debated ultimate strengths along the long axis the the femur, known as the longitudinal direction. Some materials, such together bone and also wood, have different ultimate staminas along various axes. The can be fried compressive strength for bone follow me the short axis (transverse direction) is 131 MPa, or around 36% less than the 205 MPa longitudinal value. Products that have various properties along different axes are recognized as anisotropic. Materials that law the exact same in all directions are referred to as isotropic.

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An amazing fact to complete up this chapter: when a human stands the femur in reality experiences compressiveand tensile emphasize on various sides of the bone. This occurs since the structure of the i know good socket applies the load of the body load off come the side fairly than directly along the lengthy axis the the bone.

Both tension and also compressive stresses are used to the Femur while standing. Photo Credit: Blausen clinical via Wikimedia Commons