Resistance-deflection function

Flexural member design requires the determination of (1) the design blast loads, (2) the initial design cross-section, (3) an idealized resistance deflection function, (4) the calculated response (maximum deflection) and, (5) allowable ultimate deflection and (6) design for shear. 

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the trial cross-section. Figure 4a shows a typical design resistance-deflection function with elastic stiffness, Kg (psi/in), elastic deflection limit, Xg (in) and ultimate resistance, r.. (psi). The stiffness is determined from a static elastic analysis using the average moment of inertia of a cracked and uncracked cross-section. (For design... 

The increased impulse capacity of a structure is proportional to the square root of the increase in the area under the resistance-deflection curve. The effect of mass can be easily shown with the following equation for the impulse capacity of a ductile element with large allowable deflection and a perfectly plastic resistance function (as shown in Figure 4b). 

Shaft deflection is the result of an external radial load. The external radial loading originates with the pump operator or proee.ss when the pump runs away from its best effieieney point on the curve. The resistance to deflection is a function of the shaft s overhang length and its diameter. The deflection resi.stanee, also called the flexibility laetor, is known as the L/D laetor. 

The polycarbonate glazing is modeled as a simply supported plate subjected to nonlinear center deflections up to 15 times the pane thickness. Using the finite element solution of Moore (Reference 4), the resistance function is generated for each pane under consideration. Typically, the resistance is concave up, as illustrated for typical pane sizes in Figure 1. This occurs because membrane stresses induced by the stretching of the neutral axis of the pane become more pronounced as the ratio of the center pane deflection to the pane... 

In many cases, the dynamic amplification factor or the ratio of static load to dynamic load capacity will exceed two. This is because of the concave up shape of the resistance function and the mobilization of membrane resistance at large deflection to thickness ratios. Because of this phenomenon, it is unconservative to assume the blast capacity of polycarbonate glazing to be no less than one half of its static pressure load capacity. 

These force versus deflection relationships are usually nonlinear (due to materials or geometry) and are called resistance functions. They are an essential input parameter for the analysis of equivalent single degree of freedom (SDOF) systems, Resistance functions are not usually needed for analyses of multi-degree of freedom (MDOF) systems. Material models employing nonlinear stress versus strain data, as discussed in Chapter 5, are used in MDOF systems. 

Structural dements resist blast loads by developing an internal resistance based on material stress and section properties. To design or analyze the response of an element it is necessary to determine the relationship between resistance and deflection. In flexural response, stress rises in direct proportion to strain in the member. Because resistance is also a function of material stress, it also rises in proportion to strain. After the stress in the outer fibers reaches the yield limit, (lie relationship between stress and strain, and thus resistance, becomes nonlinear. As the outer fibers of the member continue to yield, stress in the interior of the section also begins to yield and a plastic hinge is formed at the locations of maximum moment in the member. If premature buckling is prevented, deformation continues as llic member absorbs load until rupture strains arc achieved. 

Variation in internal resistance can be related to the strain because stress in a member is a function of the strain experienced at a given point. Deformation of a key point on the member can also be related to the strain producing a relationship between resistance and deflection as shown by the curve in Figure 5.1, Elastic resistance is the level at which the material reaches yield at the location of maximum moment in the member, Beyond the point of first yield of a member, plastic regions are formed in the section and an clastic-plastic condition occurs. Internal resistance... 

Soil resistance is a non-linear function of pile deflection and depth below the ground surface. The soil resistance can be expressed as follows ... 

Reinforced pol)nners are those to which fibers have been added that increase the physical properties—especially impact resistance and heat deflection temperatures. Glass fibers are the most common additions, but carbon, graphite, aramid, and boron fibers are also used. In a reinforced polymer, the resin matrix is the continuous phase, and the fiber reinforcement is the discontinuous phase. The function of the resin is to bond the fibers together to provide shape and form and to transfer stresses in the structure from the resin to the fiber. Only high-strength fibers with high modulus are used. Because of the increased stiffness resulting from the fiber... 

Rigidity r9- ji-d9-te (1624) n. The ability of a structure to resist deformation under load. It is a function of both the material s modulus of elasticity and, often more critically, of the geometry of the structure. In a loaded beam, whatever the load distribution or type of beam supports, the maximum deflection is inversely proportional to the product, El, of the material s elastic modulus and the moment of inertia of the beam s cross-section about its neutral axis. The term rigidity is often applied loosely to materials themselves without reference to a particular structure when what the speaker actually has in mind is the elastic modulus. See also section modulus. 

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