“In human anatomy, the femur (thigh bone) is the longest and largest bone. Along with the temporal bone of the skull, it is one of the two strongest bones in the body. The average adult male femur is 48 cm (18.9 in) in length and 2.34 cm (0.92 in) in diameter and can support up to 30 times the of an adult.”
When you place an object on top of a structure, the object’s weight tends to compress the structure. Any push that tends to compress a structure is called a . The average weight among adult males in the United States is 196 lbs (872 N). According to the statement that the femur can support 30x body weight, the adult male femur can support roughly 6,000 lbs of compressive force! Such high forces are rarely generated by the body under its own power, thus motor vehicle collisions are the number one cause of femur fractures.
When you hang an object from a structure the object’s will tend to stretch the structure. The structure responds by providing a force to hold up the object. Tension forces are produced in response to materials being stretched. Non-rigid objects like ropes, cables, chains, muscles, tendons, can effectively provide tension forces only, while rigid object can supply and tension forces. For example, the biceps muscle is providing a tension (T) force on the thumb-side forearm bone (radius bone).
The maximum or forces that a bone can support depends on the size of the bone. More specifically, the more area available for the force to be spread out over, the more force the bone can support. That means the maximum forces bones, (and other objects) can handle are to the c of the bone that is (90°) to the direction of the force. For example, the force that the femur can support vertically along its length depends on the area of its horizontal cross-section which is roughly circular and somewhat hollow (bone marrow fills the center space).
Larger bones can support more force, so in order to analyze the behavior of the bone material itself we need to divide the force applied to the bone by the minimum (). This quantity is known as the (σ) on the material. Stress has units of force per area so the units are (N/m2) which are also known as . Units of pounds per square inch (PSI, lbs/in2) are common in the U.S.
Estimate the stress within a 1.0 cm x 2.0 cm Lego block when you step on it with full body in units of pb_glossary id=”3977″]Pascals[/pb_glossary]. [Hint: We want the result in units, so convert the length and width to meters before calculating the and use SI units for your weight.]
Ultimate Strength of the Femur
The maximum that bone, or any other material, can experience before the material begins or is called the . Notice that material strength is defined in terms of stress, not force, so that we are analyzing the material itself, without including the effect of how much material is present. For some materials the ultimate strength is different when the stress is acting to crush the material () versus when the forces are acting to stretch the material under , so we often refer to ultimate tensile strength or ultimate compressive strength. For example, the ultimate compressive strength for human femur bone is measured to be 205 MPa (205 Million Pascals) under compression along its length. The ultimate tensile strength of femur bone under tension along its length is 135 MPa. Along with bone, concrete and chalk are other examples of materials with different compressive and tensile ultimate strengths.
Try to crush a piece of chalk by using your fingers to push on the ends and compress it along the long axis, no bending allowed. Any luck?
Now use your fingers to break the chalk by pulling it apart, straight along the long axis, again no bending allowed. Any luck?
Record your results and explain what they tell you about the compressive and tensile of chalk.
Compare and contrast the behavior you observed for chalk with the known behavior of bone and concrete. Cite your sources.
Let’s check to see if the measured values for compressive agree with the claim that the human femur can support 30x the adult body , or roughly 6,000 lbs
First let’s to convert the claimed 6,000 lbs force to and work in SI units.
An approximate minimum of the femur is . (*See the bottom of this example if you are interested in learning how we approximated this value). We divide the compressive force by the cross-sectional area to find the compressive stress on the bone.
Our approximate value for the of bone that would be required to support 30x body weight was 80 MPa, which is actually less than the measured value of 205 MPa, so the claim that the femur can support 30x body weight seems reasonable.
*This is 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 two to find the femur radius, then we convert to standard units of meters.
Using the equation for the area of a circle we calculate the total area of the femur to be:
Finally we have to subtract off the area of the hollow middle part to get the net bone area. We used a ruler on the above picture of the femur cross-sections to see that the inner radius is roughly half of the outer radius, or so we calculate the missing inner area:
And subtract off the inner area from the total:
Transverse Ultimate Strength
So far we have discussed along the long axis of the femur, known as the direction. Some materials, such as bone and wood, have different ultimate strengths along different axes. The ultimate compressive strength for bone along the short axis ( direction) is 131 MPa, or about 36% less than the 205 MPa longitudinal value. Materials that have different properties along different axes are known as . Materials that behave the same in all directions are called .
An interesting fact to finish up this chapter: when a person stands the femur actually experiences compressive and tensile stresses on different sides of the bone. This occurs because the structure of the hip socket applies the load of the body off to the side rather than directly along the long axis of the bone.
- "Femur" by Orthapaedics One ↵
- By Anatomography [CC BY-SA 2.1 jp (https://creativecommons.org/licenses/by-sa/2.1/jp/deed.en)], via Wikimedia Commons ↵
- "Body Measurement" by FastStats, U.S. Centers for Disease Control is in the Public Domain ↵
- "Femur Shaft Fractures" by OrthoInfo, American Academy of Orthopaedic Surgeons ↵
- OpenStax University Physics, University Physics Volume 1. OpenStax CNX. Jul 11, 2018 http://firstname.lastname@example.org. ↵
- "Effects of a Chronic Condition: Osteoporosis" by Written in Bone, Smithsonian National Museum of Natural History ↵
- "Elastic anisotropy of bone" by Rod Lakes , College of Engineering, University of Wisconson ↵
- Blausen.com staff (2014). "Medical gallery of Blausen Medical 2014". WikiJournal of Medicine 1 (2). DOI:10.15347/wjm/2014.010. ISSN 2002-4436. [CC BY 3.0 (https://creativecommons.org/licenses/by/3.0)], from Wikimedia Commons ↵
the force of gravity on on object, typically in reference to the force of gravity caused by Earth or another celestial body
reduction in size caused by application of compressive forces (opposing forces applied inward to the object).
the force that is provided by an object in response to being pulled tight by forces acting from opposite ends, typically in reference to a rope, cable or wire
a force that tends to move a system back toward the equilibrium position
having a constant ratio to another quantity
The cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point. For example, the cross-section of a cylinder - when sliced parallel to its base - is a circle
at an angle of 90° to a given line, plane, or surface
a physical quantity that expresses the internal forces that neighboring particles of material exert on each other
a system of physical units ( SI units ) based on the meter, kilogram, second, ampere, kelvin, candela, and mole
the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. It is defined as one newton per square meter
the separation of an object or material into two or more pieces under the action of stress and associated strain
the sudden and complete failure of a material under stress
the maximum stress a material can withstand
running lengthwise rather than across
situated or extending across something, (crosswise)
having a physical property that has a different value when measured in different directions
having a physical property which has the same value when measured in different directions