question: Why does the jeans break always in the same manner, first the vertical fibers, then the horizontal?
comment: The vertical fibres are under more stress more often (eg - especially at the front bend of the knee) After the first vertical fibres fray and break, this adds more load onto the other ones, so they break more easily. And this finally exposes the horizontal threads. So they'll start breaking too, eventually.
passages: The approximate value of the Jeans mass may be derived through a simple physical argument. One begins with a spherical gaseous region of radius formula_8, mass formula_9, and with a gaseous sound speed formula_10. The gas is compressed slightly and it takes a time
  
  for sound waves to cross the region and attempt to push back and re-establish the system in pressure balance. At the same time, gravity will attempt to contract the system even further, and will do so on a free-fall time,
   Section::::Influence of rock material rheology.:Example.
  
  Rocks that contain incompetent (mechanically weak) minerals such as micas and more competent (mechanically stronger) minerals such as quartz or feldspars, may develop a shear band fabric. The incompetent minerals will preferentially form the C-surfaces and competent minerals will form along the S-surfaces.
  
  Section::::Individual deformation mechanisms.
   The Jeans instability likely determines when star formation occurs in molecular clouds.
   Over time dry denim will fade, considered fashionable in some circumstances. During the process of wear, fading will usually occur on those parts of the article that receive the most stress. On a pair of jeans, this includes the upper thighs, the ankles, and the areas behind the knees.
   In the bearing joint, the bolt itself limits lateral movement of the elements by the shank of the bolt bearing upon the sides of the holes in the clamped elements. Such joints require less clamping force, because a high level of friction between the clamped surfaces is not required. The clearance between the bolt and the holes means that some lateral movement may occur before the bolt bears against the sides of the holes. 
   The statistical variation of the platelets has a negative effect on the mechanical performance (stiffness, strength, and energy absorption) because statistical variation precipitates localization of deformation . However, the negative effects of statistical variations can be offset by interfaces with large strain at failure accompanied by strain hardening . On the other hand, the fracture toughness of nacre increases with moderate statistical variations which creates tough regions where the crack gets pinned . But, higher statistical variations generates very weak regions which allows the crack to propagate without much resistance causing the fracture toughness decreases . 
   BULLET::::1. Tensile fibre failure for σ11 ≥ 0
  
  BULLET::::2. Compressive fibre failure for σ11  0
  
  BULLET::::3. Tensile matrix failure for σ22 + σ33  0
  
  BULLET::::4. Compressive matrix failure for σ22 + σ33  0
  
  BULLET::::5. Interlaminar tensile failure for σ33  0
  
  BULLET::::6. Interlaminar compression failure for σ33  0
   BULLET::::12. Corrosion products that accumulated at the faying surfaces of the dissimilar metals raised the stresses in some instances enough, with the combined corrosive action, to cause cracks to form in the strips. Such cracks were found on 24ST and Alclad 24ST strips coupled with nickel alloys or stainless steel, on Dowmetal H strips coupled with aluminum alloys or stainless steel, and on stainless-steel strips coupled with Dowmetal M.
   Most carpenter jeans are made for function, not fashion, and are usually of a softer denim than the original utilitarian jeans, with a looser fit. Carpenter jeans were quite popular in the late 1990s and early 2000s hip hop scene especially those by the Tommy Hilfiger brand who placed their trademark logo on the hammer loop.
   Section::::Manufacturing processes.:Used and distressed looks.
  
  The used or "acid wash" look is created by means of abrading the jeans and/or treating them with chemicals, such as acryl resin, phenol, a hypochlorite, potassium permanganate, caustic soda, acids etc.
  
  Ripping or distressing of jeans, though also arising naturally as a result of wear and tear, is sometimes deliberately performed by suppliers - with distressed clothing sometimes selling for more than a nondistressed pair. For example, Pucci sold "embellished mid-rise boyfriend jeans" for £600 (US$860).
  
  Section::::Manufacturing processes.:Sandblasting or abrading with sandpaper.
   where G is the gravitational constant, formula_10 is the sound speed, and formula_14 is the enclosed mass density.
  
  It is also the distance a sound wave would travel in the collapse time.
  
  Section::::Fragmentation.
  
  Jeans instability can also give rise to fragmentation in certain conditions. To derive the condition for fragmentation an adiabatic process is assumed in an ideal gas and also a polytropic equation of state is taken. The derivation is shown below through a dimensional analysis:
   Levi Strauss, as a young man in 1851, went from Germany to New York to join his older brothers who ran a goods store. In 1853, he moved to San Francisco to open his own dry goods business. Jacob Davis was a tailor who often bought bolts of cloth from the Levi Strauss & Co. wholesale house. In 1872, Davis wrote to Strauss asking to partner with him to patent and sell clothing reinforced with rivets. The copper rivets were to reinforce the points of stress, such as pocket corners and at the bottom of the button fly. Levi accepted Davis's offer, and the two men received US patent No. 139,121 for an "Improvement in Fastening Pocket-Openings" on May 20, 1873.
   Assume there is no clearance or slack but in actual, knuckle pin is loose in forks to permit angular moment of one with respect to other, so it is subjected to bending moment in addition to shear, consider uniformly distributed load along the portion of pin.
  
  Taking moment about axis XX
  
  Section modulus,
  
  Maximum bending stress, σ
  
  Here,we check the pin in bending and find the value of d
  
  (3) Design of single eye :
   It was later pointed out by other astrophysicists that in fact, the original analysis used by Jeans was flawed, for the following reason. In his formal analysis, Jeans assumed that the collapsing region of the cloud was surrounded by an infinite, static medium. In fact, because all scales greater than the Jeans length are also unstable to collapse, any initially static medium surrounding a collapsing region will also be collapsing. As a result, the growth rate of the gravitational instability relative to the density of the collapsing background is slower than that predicted by Jeans' original analysis. This flaw has come to be known as the "Jeans swindle".
   Dry denim also varies in weight, typically measured by the weight of a yard of denim in ounces. 12 oz. or less is considered light denim, 12 oz. to 16 oz. is considered mid-weight, and over 16 oz. is considered heavyweight. Heavier denim is much more rigid and resistant to wear, but can also take a larger number of wears to break in and feel comfortable.
  
  Patterns of fading in jeans caused by prolonged periods of wearing them without washing are a way of "personalizing" the garment.
  
  These patterns have specific names:
   The diagonal and vertical members form the "truss web", and carry the shear stress. Individually, they are also in tension and compression, the exact arrangement of forces is depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression.
   The stress given by this equation is exact, knowing that the cross section is not adjacent to the point of application of the load nor having holes for bolts or other discontinuities. For example, given an 8 x 11.5 plate that is used as a tension member (section a-a) and is connected to a gusset plate with two 7/8-inch-diameter bolts (section b-b):
  
  The area at section a - a (gross area of the member) is 8 x ½ = 4 in
   All materials have varying physical and mechanical properties. As a materials ultimate tensile strength increases, this does not lead to an increase in fatigue strength. This is not the case when evaluating materials that do not contain welded joints. Therefore stress-cycle curves for welded joints cannot be correlated to the materials ultimate tensile strength. Most design information has been developed for structural steels.
  
  Section::::Factors Affecting Fatigue.:Welding Process.
   Research into the causes of vibration induced self-loosening of threaded fasteners spans six decades and the causes of self-loosening are now well understood. It was pioneering experimental research into the behaviour of bolted joints under transverse loads, conducted by German engineer Gerhard Junker in the late 1960s which underpins modern theories on self-loosening behaviour.
   Despite most jeans being "pre-shrunk", they are still sensitive to slight further shrinkage and loss of color from being washed. The Levi Strauss company recommends avoiding washing jeans as much as possible. Carl Chiara, Levi Strauss director of brand and special projects, has a credo: The less you wash your jeans, the better your jeans become. These and other suggestions to avoid washing jeans where possible have encountered criticism. Cory Warren, editor of "LS&Co. Unzipped", clarifies in a response to such a criticism:
   Section::::Toughening Mechanisms.:Damage Competition Theory.
  
  The damage competition theory models the relative contributions of shear yielding and craze failure, when both are present. there are two main assumptions: crazing, microcracks, and cavitation dominate in brittle systems, and shearing dominates in the ductile systems. Systems that are in between brittle and ductile will show a combination of these. The damage competition theory defines the brittle-ductile transition as the point at which the opposite mechanism (shear or yield damage) appears in a system dominated by the other mechanism.
  
  Section::::Toughening Mechanisms.:Characterization of Failure.
   where formula_6 is the universal gravitational constant, formula_14 is the gas density within the region, and formula_15 is the gas number density for mean mass per particle (formula_16 g is appropriate for molecular hydrogen with 20% helium by number). When the sound-crossing time is less than the free-fall time, pressure forces temporarily overcome gravity, and the system returns to a stable equilibrium. However, when the free-fall time is less than the sound-crossing time, gravity overcomes pressure forces, and the region undergoes gravitational collapse. The condition for gravitational collapse is therefore:
  
  The resultant Jeans length formula_18 is approximately:
   BULLET::::- loading members only in pure compression or pure tension, meaning the structure will only fail if the cables yield or the rods buckle
  
  BULLET::::- preload or tensional prestress, which allows cables to be rigid in tension
  
  BULLET::::- mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases
  
  Because of these patterns, no structural member experiences a bending moment. This can produce exceptionally rigid structures for their mass and for the cross section of the components.
   Normal stress occurs in many other situations besides axial tension and compression. If an elastic bar with uniform and symmetric cross-section is bent in one of its planes of symmetry, the resulting "bending stress" will still be normal (perpendicular to the cross-section), but will vary over the cross section: the outer part will be under tensile stress, while the inner part will be compressed. Another variant of normal stress is the "hoop stress" that occurs on the walls of a cylindrical pipe or vessel filled with pressurized fluid.
  
  Section::::Simple stress.:Simple shear stress.
   Frank Mechaly draws upon his earliest memories of spending time at the factory with his father as the inspiration for his lifelong passion for designing jeans. Speaking in a candid interview he says: "I remember one particular Saturday morning back in the seventies, riding to the jeans factory with my father in his Porsche. I used to have free run of the entire factory as a child and in these days before stonewashing came about, I would go into one particular room and lie down in a huge pile of fresh denim, which has a very distinctive scent, and I knew at that time that I wanted to spend the rest of my life making jeans."
  