Beams stiffness factor

Stiffness For an isotropic material with a modulus of elasticity E, the bending stiffness factor (El) of a rectangular beam b wide and h deep stiffness is ... 

An example of the foregoing is an RP beam [Figure 8.17 (c)] made up of five layers having three different moduli of elasticity, and three different strengths. The neutral axis, found by applying the neutral axis X equation, is 0.415 in fi-om the bottom of the cross-section. Distances from the neutral axis to the centers of the individual layers are computed, and the stiffness factor El calculated. This is found to be ... 

If in the service of a component it is the deflection, or stiffness, which is the limiting factor rather than strength, then it is necessary to look for a different desirability factor in the candidate materials. Consider the beam sim-ation described above. This time, irrespective of the loading, the deflection, S,... 

Equivalent mass, stiffness and loading arc obtained through the use of transformation factors. Several widely used texts on blast design such as /yny, (Chapter 5) and TM 5-1300 (Chapter 3) contain tabulated transformation factors for typical structural elements such as beams and slabs. The derivations of the equations for these transformation factors are also given by these references. Transformation factors used to obtain appropriate properties for the equivalent SDOF system are as follows ... 

One of the most important parameters of the property of the section is its moment of inertia. It is a measnre of the strength and stiffness of a board (generally, of a beam). The moment of inertia is a rigidity factor, and it is defined by the section s... 

These results can be compared to the same set of results obtained from the study on beam specimens (SLCOl and SLC02) in Section 8.2, which were subjected to four-point bending during 60 and 120 min fire exposure from the underside, see Table 8.6. In the former study, six-cell specimens were used in contrast to the four-cell specimens used here. The bending stiffnesses obtained from Section 8.2 were therefore corrected by a factor of 4/6 in order to make them comparable. At the end of fire exposure, the bending stiffness of the still-hot specimens (SLCOl/02) dropped to 46% and 43% of the initial value, which almost matched the values obtained for the column specimens. The post-fire stiffnesses (64% and 60%), however, were slightly lower than those of the column specimens (76% and 70%). 

The Gamma method is named after the caitical factor Gamma y, which describes the relative stiffness of the elastic shear connection between the two members which form the bipartite beam. In a normal glulam beam, where the laminates are connected together with very stiff adhesive layers, y is 1.0 where there is no adhesive at all, and the two laminates are in no way connected to each other, y is zero. Our calculations indicate that the bipartite beam will attain the above optimal bending resistance only if the y value of the connection between the two members attains the corresponding ideal value ... 

The theory further explains that the total bending stiffness E/ef of the bipartite beam is the sum of the bending stiffnesses of the two component members and the Steiner component corrected with the y-factor. The calculations lead to the following result ... 

In Equation (3) the first and third terms in the square brackets, when multiplied by the factor outside these brackets, represent respectively the flexural and shear deflections of a simply supported beam carrying a point load at its centre. The second term accounts for the fact that the beam is not simply supported but forms part of a frame with identical semi-rigid beam-column Joints. Also in Equation (3), the a (= EI/GA) and p (= EI/K, where K is the joint stiffness) parameters reflect the contributions of shear deformation and semi-rigidity respectively to the mid-span deflection. Similar expressions have been derived for the beam translation under sway mode loading and the corresponding rotations at the beam-column joints and pinned bases. Some of these expressions have been used to predict the frame deformations described in the next section. 

Dr. Duan s research interests cover areas including inelastic behavior of reinforced concrete and steel structures, structural stability, seismic bridge analysis, and design. With more than 70 authored and coauthored papers, chapters, and reports, his research focuses on the development of unified interaction equations for steel beam-columns, flexural stiffness of reinforced concrete members, effective length factors of compression members, and design of bridge structures. 

Consider, for example, the maximizing factor for a light, stiff beam and give it a value of... 

Due to the cross-sectional asymmetry of the SCC beam, the response will be different for positive and negative moments. As a result, a hinge must discern the load paths to model the hysteretic behavior of SCC beam for an arbitrary cyclic loading. Apart of the cross-sectional asymmetry, the hysteretic mles employed for the complete element need to take into account factors such as the strength deterioration and the stiffness degradation. 

The bending stiffness of a homogeneous beam of material 1 is ,/. Thus, the effective bending stiffness of the sandwich beam has been reduced by the factor a, by replacing the core by material 2 with a lower modulus 2 but with a lower density P2. However, the stiffness-to-weight ratio has been increased as shown by Example 9.2. 

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