I need an Inplane property E1 and E2 , since I used bidirectional woven mat E1 and E2 are same. So I determined equivalent properties 'E' through static bending deflection test. Is it correct?

You use equivalent single layer (ESL) theories with shear deformation for that but you miss all the information concerning strain and stress fields inside the beam. As reported by J. Ye, the ESL are capable to compute with a satisfactory degree of accuracy global response of the sandwich beam such as deflexion, mode shapes, etc, but not for stresses and strains. For that you should use independent layer theories (zig-zag,

layerwise or combined models). If you intend to use commercial software you can construct layered models using a layered scheme of conventional models.

The Euler-Bernoulli assumptions can give you bad results for higher natural frequencies in composite beams and plates. You can check this in my paper: Eigenfrequency analysis of completely free multilayered rectangular plates using a higher-order model and Ritz technique

Classical beam theory EBT gives acceptably correct results for beams ans plates with higher aspect ratios i.e. for thin structural elements. However for thick and moderately thick structures it gives enormous errors upto 30 %. So if the beam under consideration is having a/h ratio exceeding 10, results will be acceptably correct for displacements and inplane stresses. However, transverse stresses are discontinuous through the thickness contrary to the elasticity solutions. In present example, as aspect ratio is 17.31, therefore the global response of the beam will be predicted acceptably correct using EBT.

Eshwar Could you expand 'a' and 'h' because i have doubt in the ratio.

Jose Could you send me your paper so that I can clarify my doubts? And also you said that higher modes can't capture by EBT ,but the higher modes in the sense which mode ? Because I'm using first five modes.

The pre-print if the paper is in my profile, but I'll send you the post-print. The better way to test if you get good results with EBT and your code is to do a 3D analysis with a commercial package of FE. Usually, the results get worst with the degree of anisotropy you have on your composite.

No . I've developed my code for 1D problem with transversely isotropic material.

Accuracy of using a theory directly depend on relative thickness. If beam or plate are thin you can use EB theory. because changing of transverse properties are negligible and quantity of transverse shear in both surface(up & down) is zero. therefore the quantity of transverse shear stress through the thickness is small. the difference of various theory is in determining the transverse shear stress that in EB we neglect transverse shear stress. in timoshenko we assume it constant and in HSTT we assume it third order because changing shear stress through thickness.

In this case you can use EB theory and result is good and accurate.

a = Length of beam or Smaller lateral dimension of rectangular plate.

h = Thickness of beam or plate

For static analysis I agree with Eshwar and as your beam is very slender, you do not introduce a large error by neglecting the shear deformation of the beam.

But for dynamic analysis you should be careful, as José pointed out. The Euler-Bernoulli Beam theory does not only neglect the shear deformation, but also the rotational inertia of the infinitesimal beam elements, which will affect particularly the higher frequency modes.

You can find a complete derivation and discussion of EB and Timoshenko beams for dynamic simulation in my PhD-thesis: " Untersuchung der dynamischen Eigenschaften von Balken mit fraktionalen Stoffgesetzen " (unfortunately only in German).

In composite laminates consisting of plies in various directions, the bending stress will distribution across the beam thickness will be discontinuous i.e in zig-zag form changing at each ply interface. However, if the plies are of the same direction as in your case of orthogonal woven laminate, the stress pattern will be contuinuos. AS the EBT gives max stress at top and bottom plies, thus it can be used in both cases for bending stress calculation at top and bottom plies. Further, in composites, the weak resin rich interface is normally susceptible to failure due to higher interlaminar shear stresses in beams, thus 1D formulation is incapable to capture the interlaminar shear stress distribution. You can consult my paper title: Finite-element modelling of bending of CFRP laminates-multiple delaminations.

Thus the shear effects cannot be neglected even in slender beam made of composite laminates because of the weaker resininterfaces. Further, there is also shear stress concentrations at the indenter and roller supports of the beam which is usually more than the shear strength of the resin interface. These stresses cause failure in composite beams in the form of delamination, Such behavior is elaborated in the above reference.