Simple supported beam

Plastic composite mechanics in conjunction with structural mechanics can be used to derive explicit equations for the structmal response of simple structural elements. These explicit expressions can then be used to perform parametric studies (sensitivity analyses) to assess the influence of the hybridization ratio on structural response. For example the structural response (behavior variables) equations for maximum deflection, buckling load and frequency of a simply supported beam made from intraply hybrids are summarized in Figure 6.7 Flexural modulus is used to determine the maximum deflection, buckling load, and frequency of a simple supported beam made from intraply hybrids. 

Simple supported beam, load at center of beam. Beam is supported at both ends. To calculate the maximum deflection for a beam supported at both ends and center-loaded, use... 

Simple supported beam, two equal loads symmetrically located between center and the two supported ends... 

Simple supported beam, load spread uniformly along beam length... 

Structural response (behavior variables) equations for maximum deflection, buckling load and frequency of a simply supported beam made from intraply hybrids are summarized in Fig. 4.39 Flexural modulus is used to determine the maximum deflection, buckling load, and frequency of a simple supported beam made from intraply hybrids. 

A uniform, rectangular-section beam of fixed width w, unspecified depth d, and fixed length L rests horizontally on two simple supports at either end of the beam. A concentrated force E acts vertically downwards through the centre of the beam. The deflection, 8, of the loaded point is... 

Packed-bed supports. A simple support for a bed of lVfc-in pall rings might consist of a bar grid, with Vi-in-thick bars, set on 1 inch center. The grid itself (see Fig. 7.7) would be supported by two 6-in-wide I-beams. The open area of each component is... 

Rectangular beam of width b To simple supports Single concentrated load P at 3 PL PL3 6 dy... 

Rectangular beam of width b Two simple supports Two equal loads P/2 at 1/3 PL 23 PL3 108 dy... 

Let us continue this discussion using the simple example introduced at the beginning of Section 5.6. The ultimate load of a beam in a steel framed building was calculated using simple plastic theory, and assuming simple supports, so that... 

The use of structural and loading symmetry to show that a beam with one clamped support is equivalent to another beam with only simple supports (a) a tip loaded cantilever beam is equivalent to a simply supported beam (b) a propped cantilever beam Is equivalent to a two-span simply supported beam (c) load versus support rotation response of a two-span, simply supported continuous 102 x 102 x 6.4 mm pultruded GFRP WF beam (reproduced with permission of Net Composites Ltd (Turvey, 2011)). 

Compared to common monolithic beams, composite beams with deformable shear connection present additional difficulties. Even in very simple structural systems (e.g., simply supported beams), complex distributions of the interface slip and force can develop. Different finite elements of composite beams with deformable shear connection have been developed and presented in the literature (Spacone El-Tawil 2004, Dall Asta 8c Zona 2004). These elements include suitable models describing section deformations in order to compute the section force resultants of steel-concrete composite members. This requires the use of realistic material constitutive models for beam steel, reinforcement steel, concrete, and shear-slip behaviour of the studs connecting the two structural components (Zona et al. 2005, 2006, Barbato et al. 2007). 

Figure 2.2 a) shows a simple cantilever beam with a built-in support at This type of support provides a resisting couple as well as horizontal constraint as shown in the free body diagram [Fig. 2.2 (b)]. A couple is a moment consisting of two equal opposing forces (F ) separated by a perpendicular distance (c) (a pure twisting action). 

The Charpy test and the Izodtest are both pendulum-type impact tests. The difference between these two tests is essentially the orientation of the sample. In the Charpy test, or simple-beam method, the sample is supported at both ends, but is not held down, as shown on the left in Figure 15.30. In the Izod test, or cantilever beam method, the sample is supported on one end in a vice, as shown on the right in Figure 15.30. In both tests the sample is at the bottom of the pendulum arc and the amount of energy absorbed by the sample is measured. 

Flexural Properties. Both flexural modulus and flexural strength values were obtained. These values were measured at 23 °C and also over a range of temperatures for the MBAS polymer (see Figure 4). In the flexural tests, a molded bar is tested as a simple beam, the bar resting on two supports, and the load is applied midway between. The test is continued until rupture or 5% strain, whichever occurs first. The test fixture is mounted in a universal tester, and the tester is placed in an appropriate temperature environment. 

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