Slenderness ratio

Combinations of D, k and L.., for various Tr values are computed (Table 1). Next, the slenderness ratio (12 L,.,/D,) is calculated. Choices in the range of 3 to 4 are most common (Table 1). Plot results and choose a reasonable size with a diameter greater than that determined by gas capacity line, Fig. 12. In this case, a 36-in. by 10-ft separator provides slightly more than 3 min retention time, a 30-in. by 10-ft separator provides about 2 min and a 36-in. by 7 6-ft vessel provides about I min. 

Compute slenderness ratio (12A,VA,). Choices in the range of 3 to 5 are common. 

General buckling in a slender column with a slenderness ratio, L/D, greater than 100, occurs when it is subjected to a critical compressive load. This load is much lower than the maximum load allowable for compressive yield. Although this problem can be easily solved using Euler s equation1, which predicts the critical load applied to the slender column, it lends itself very well to illustrate dimensional analysis. 

Bubble Deformation A 5-mm radius bubble is placed in a viscous liquid of 0.2 lbf s/in2 and surface tension of 22 dyne/cm. Calculate the shape of the bubble, the half-length, and slenderness ratio of the bubble at shear rates 1, 10, and... 

For a vertical condensing liquid film, scale analysis of the 2-dimensional constant-property conservation equations of mass, momentum and energy, with appropriate boundary conditions, shows that Rafii is a measure of the slenderness ratio L/d of the film (18). Here L is taken as the streamwise length of the condensation film and d an average film thickness. This interpretation is valid in the limit where the momentum equation is a balance of viscous and gravitational forces. Under such conditions, a velocity scale is... 

Introducing the slenderness ratio to eliminate d, we get the final form of our first criterion... 

This defines the Marangoni number Ma. The expression for the slenderness ratio of our gravity-driven film is again used in Equation 9. We call this Criterion B. Having now introduced the reference velocity U., we note that Criterion A as expressed by Equation 7. is the ratio U j./Uj.. 

Mean values in particle dimension, thickness, length and slenderness ratio (length/thickness), used in this test are shown in Table 1. These mean values were based on two hundred measurements of each furnish type and calculated using the Weibull distribution function. 

These are prepared with specialist flaking equipment that can use small diameter logs. Initially this was from species having no other use, but as capacity has grown alternative wood sources have been used. The process evolved from the waferboard manufacture that used thin flakes or wafers to form a panel where the wafers performed as small veneers. The increased slenderness ratios of strands resulted in improvements in both strength and directional properties so that OSB became an alternative to plywood. The reduced width of the strands compared with wafers allowed them to be produced from smaller diameter wood. 

MDF is also produced from chips, but increasingly sawdust and shavings are used as fibre sources. As the name suggests the particles in this case are fibres or fibre bundles characterised by a high slenderness ratio, typically 80-100 1 for whole individual fibres. Most of the fibres in sawdust and shavings are damaged in the... 

It is these two characteristics - the slenderness ratio, and the overall small size of the particles - that have lead to the distinctive features of the MDF proeess. 

The major difference between the fibres used to make medium density fibreboard and the particles used to make particleboard is the greater slenderness ratio of the fibres. This is the reason why mechanical blenders designed for particleboard were not satisfactory for MDF. It is also the reason why the bulk density of fibre is low, particularly with fibres prepared from a chipped material. The fibres form networks that are quite strong, with fibres able to span considerable distances. The mats formed from such fibres hold together so that formed or even trimmed edges hold their shape. There is no requirement for tack from the resin to hold the fibre mat together. 

USA standards For a right prism the preferred dimensions are 12.7 mm For rod slenderness ratio should be in... 

Structural parameters such as the slenderness ratio frequently govern what can and cannot be done. An engineer would be hard pressed to find a reputable contractor willing to build a 40-m-long column, half a meter in diameter. 

Particles as raw material for particleboards show a great variety in wood species, origin, method of preparation, age, and especially size and shape. If wood is ground into particles, a mixture of particles of very different sizes and shapes is always obtained. Particles can be described in a simple way as squared flat pieces with certain values for length / (mm), width b (mm), thickness d (mm), and slenderness ratio s = //d. The volume of a particle is then given as... 

There are two kinds of failure due to buckling. The first, general buckling, involves bending of the axis of the cylinder, resulting in instability. This is the type addressed by Euler and designed for by a slenderness ratio method. 

For short and intermediate cylinders the critical stress is independent of length. For long cylinders the length of the cylinder is a key factor. The range of cylinders whose slenderness ratios are less than Euler s critical value are called short or intermediate columns. 

Cross-bracing. Cross braces are tension and compression members. They may be pinned at the center or not. If the slenderness ratio of the cross brace exceeds 120, then the cross-bracing must be pinned at the center. 

Allowable compressive stress, F , based on slenderness ratio. 

---