Beams with web openings can include cellular beams fabricated from rolled sections or plate girders with circular or rectangular openings cut in the webs. Typical long span floor beams of this nature are designed to act compositely with the floor slab, as shown in Figure 1, greatly increasing their load carrying capabilities.<\/p>\n
![\"\"](\"http:\/\/www.newsteelconstruction.com\/wp\/wp-content\/uploads\/2012\/10\/Fig1.jpg\" "\\"Fig1\\"")
<\/a>Figure 1: Typical beam with web openings<\/p><\/div>\n
<\/a>Figure 2: Typical model of the forces and moments acting on the web post<\/p><\/div>\n
<\/a>Figure 3: Web post buckling behaviour observed in a cellular beam test. (Photograph courtesy Westok Ltd)<\/p><\/div>\n
<\/a>Figure 4: Equivalent strut model<\/p><\/div>\n
<\/a>Figure 5: Vierendeel bending of a stiffened rectangular opening<\/p><\/div>\n
<\/a>Figure 6: Relative values of material properties of steel with temperature<\/p><\/div>\n
The use of asymmetric sections is also common, as this allows the weight of the beam to\u00a0 be reduced by removing steel from the top of the section where it is less effective.<\/p>\n
Structural Behaviour \u00a0<\/strong><\/p>\n The structural behaviour of beams with web openings is relatively complex and involves five main failure modes which are included in the design model for ULS design at room temperature and in fire conditions. The modes of failure are described briefly below, for a fuller explanation of the structural behaviour reference may be made to Lawson et al(1)<\/sup> or P068(2)<\/sup>.<\/p>\n Global bending & vertical shear \u00a0<\/strong><\/p>\n The global bending capacity of the beam is calculation at the centre of each opening and is based on a reduced cross sectional area. A composite beam with large openings tends to resist bending predominantly by tension in the bottom tee and compression in the concrete. The global bending capacity and the vertical shear capacity are rarely the critical modes of failure in cellular beams. In bending the utilisation of the bottom flange of the section will depend on the ability of the web posts to transfer horizontal shear. In\u00a0 beams with closely spaced openings the web post will often govern the load carrying capacity.<\/p>\n The shear resistance of a cellular beam takes account of the contribution of the web and flange for rolled sections and the concrete slab. The precise distribution of shear between the top and bottom tees is determined from the analysis procedure and must be compatible with the vierendeel bending capacity of the tees.<\/p>\n Web Post bending and horizontal shear \u00a0<\/strong><\/p>\n The model shown in Figure 2 shows the forces and moments acting on the web post\u00a0 between adjacent openings. Horizontal shear forces are developed in the web post in order to transfer the incremental tension force to the bottom tee. Web posts in\u00a0 asymmetric beams will also be subject to in-plane moments in order to maintain equilibrium\u00a0 between the top and bottom tees.<\/p>\n Web Post Buckling \u00a0<\/strong><\/p>\n Due to the shear forces transferred across the web posts between openings failure can\u00a0 occur due to out of plane buckling, as illustrated by Figure 3. The tendency for the web post to buckle will depend on the width of the web post the height of the opening and the d\/t ratio of the web.<\/p>\n The web post buckling model currently preferred is based on the concept of an equivalent strut, as shown in Figure 4. This model has been calibrated against test results and finite element analysis for cold and fire design.<\/p>\n Vierendeel bending<\/strong><\/p>\n Vierendeel bending occurs due to the transfer of shear forces across an opening, which results in the development of local moments in the top and bottom tees. The bending resistance of the top tee can be based on the composite cross section where appropriate. When calculating these local bending resistances the moment capacity will be reduced to account for the presents of axial forces and shear due to global bending behaviour. Figure 5 shows vierendeel bending of a stiffened rectangular opening.<\/p>\n Fire conditions \u00a0<\/strong><\/p>\n A similar structural model is adopted for fire design taking into account the variation of the material properties with temperature. The temperature distribution for cellular beams with various forms of fire protection needs to be determined from fire testing. The structural behaviour of the cellular beam may differ in fire conditions compared to room temperature conditions. The mode of failure observed in fire may be different to that observed for room temperature design. The principle difference will be the buckling behaviour of the web posts which is influenced by the variation of yield strength and\u00a0 elastic modulus with temperature. Figure 6 shows the variation of yield stress & elastic modulus with temperature. The greater reduction in elastic modulus with temperature compared to yield strength means that the buckling behaviour can become more significant to structural performance as the temperature of the member increases.<\/p>\n Thermal distribution \u00a0<\/strong><\/p>\n For the fire limit state, the structural model must assume a temperature distribution on the beam cross section in order for the capacity of the section to be calculated. From observations of previous fire tests on beams, the non-perforated web will generally be at a higher temperature relative to the flanges, due to the difference in thickness between these elements.<\/p>\n Figure 7: Thermal distribution<\/p><\/div>\n Figure 8: Relationship between bottom flange temperature and webpost temperature<\/p><\/div>\n However, the web posts between openings have been observed to experience a further increase in temperature relative to a non-perforated web, which accentuates the effect of the change of material properties with temperature.<\/p>\n Figure 7 shows the temperatures that must be determined for a cellular beam in order to allow the structural model to be applied to the fire design case. These temperatures are normally taken as relative values with respect to the bottom flange temperature, which is used as a reference point.<\/p>\n The temperature of the web post has been found to be dependant on the width of the web post and also the fire protection material used to protect the beam. Figure 8 shows the\u00a0 relationship between web post temperature and bottom flange temperature for a number of test specimens covering a range of web post widths and coating types. From these test results the generic relationship used in the RT1085(3)<\/sup>\u00a0structural model has been derived and is shown as the solid line in Figure 8.<\/p>\n A similar relationship to that shown in Figure 8 has been observed for sprayed\u00a0 cementatious fire protection materials(4)<\/sup>. At present no data is available for board\u00a0 protection systems.<\/p>\n Limiting Temperatures \u00a0<\/strong><\/p>\n As the mode of failure of cellular beams in fire conditions can change to web post buckling due to the combined effect of changing material properties and non-uniform\u00a0 temperatures, the limiting temperature of this type of section will depend on the performance of the fire protection material used to protect it. Some fire protection materials perform better than others in terms of their ability to limit the increase in web post temperature.<\/p>\n It is not adequate to base the fire protection requirements of cellular beams on room temperature structural analysis using the concept of load ratio, as is the case with plain beams. An elevated temperature structural analysis which takes account of temperature\u00a0 distribution and instability affects must be conducted for cellular beams.<\/p>\n ASFP Testing Protocol \u00a0<\/strong><\/p>\n The purpose of the testing protocol is to determine suitable thermal data to enable a product specific version of the web post bottom flange temperature relationship to be\u00a0 determined. This can then be used as part of a structural analysis in order to determine appropriate limiting temperatures for design purposes.<\/p>\n<\/a><\/a>