- Pronouns
- he/him
- TNP Nation
- El_Fiji_Grande
- Discord
- El Fiji Grande (#3446)
Axial Stress
Axial stress (?) is defined as the normal force (P) per unit cross-sectional area (A). (?=P/A). The force is the internal force found within the member, and can put the member either in tension or in compression. An assumption is made that the force creates a uniform stress distribution across any arbitrary cross section of the member. This assumption is false, but greatly simplifies the problem, and is not too far off of the correct result when analyzing stress distributions in the middle of the member.
Shear Stess
Shear stress (?) is defined as the transverse force (P) per unit cross-sectional area (A). (?average=P/A). This provides the average shear stress across the section. However, unlike axial stresses, the shear distribution cannot be assumed to be uniform across the section. The actual value of ? varies from zero at the surface of the member to ?max.
Stress Components
The blue block shown above is our standard Structures Potato. You'll see it a bit more in the future. We have selected an arbitrary dV of the structures potato, that is infinitesimally thin in each direction. A common problem in mechanics of materials is to find the stress matrix at any given point within a structure. The diagram above shows each of the different stresses of both the axial and shear varieties we will need to consider for a basic structural analysis.
The axial stresses are on the diagonal of the stress matrix, and the shear stresses are every other component. To read the subscripts, note that the first subscript denotes the direction normal to the face, and the second subscript denotes the direction of the stress. Note that if you draw a FBD, you will find that ?yz = ?zy, ?zx = ?xz, and that ?xy = ?yx. A common set of assumptions used in this sort of very basic structural analysis is that the material is isotropic, linearly elastic, and homogeneous, which excludes materials such as wood and carbon fiber. This stress matrix can also be referred to as the Cauchy stress tensor.
Factor of Safety
Factor of Safety (FS) is the ratio of the ultimate load a material can carry to the allowable, working load the design is expected to carry. FS = (ultimate load)/(allowable load). A nearly equivalent definition holds that FS = (ultimate stress)/(allowable stress), but this ceases to be proportional as the load approaches the ultimate value. The first definition is preferred.
Axial stress (?) is defined as the normal force (P) per unit cross-sectional area (A). (?=P/A). The force is the internal force found within the member, and can put the member either in tension or in compression. An assumption is made that the force creates a uniform stress distribution across any arbitrary cross section of the member. This assumption is false, but greatly simplifies the problem, and is not too far off of the correct result when analyzing stress distributions in the middle of the member.
Shear Stess
Shear stress (?) is defined as the transverse force (P) per unit cross-sectional area (A). (?average=P/A). This provides the average shear stress across the section. However, unlike axial stresses, the shear distribution cannot be assumed to be uniform across the section. The actual value of ? varies from zero at the surface of the member to ?max.
Stress Components
The blue block shown above is our standard Structures Potato. You'll see it a bit more in the future. We have selected an arbitrary dV of the structures potato, that is infinitesimally thin in each direction. A common problem in mechanics of materials is to find the stress matrix at any given point within a structure. The diagram above shows each of the different stresses of both the axial and shear varieties we will need to consider for a basic structural analysis.
The axial stresses are on the diagonal of the stress matrix, and the shear stresses are every other component. To read the subscripts, note that the first subscript denotes the direction normal to the face, and the second subscript denotes the direction of the stress. Note that if you draw a FBD, you will find that ?yz = ?zy, ?zx = ?xz, and that ?xy = ?yx. A common set of assumptions used in this sort of very basic structural analysis is that the material is isotropic, linearly elastic, and homogeneous, which excludes materials such as wood and carbon fiber. This stress matrix can also be referred to as the Cauchy stress tensor.
Factor of Safety
Factor of Safety (FS) is the ratio of the ultimate load a material can carry to the allowable, working load the design is expected to carry. FS = (ultimate load)/(allowable load). A nearly equivalent definition holds that FS = (ultimate stress)/(allowable stress), but this ceases to be proportional as the load approaches the ultimate value. The first definition is preferred.