Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

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112 Chapter FiveDownloaded From : www.EasyEngineering.netLoad DiagramShearForceV, lbBendingMomentM, in.-lb Deflection ∆, in.P Pl Pl 3 /3ElP/2 Pl/4 Pl 3 /48EIww.EasyEngineering.nPa/l Pab/l Pb[l 2 /16 – b 2 /12]/ElP Pa Pa [3l 2 /4 – a 2 ]/6El3P/2 P[l/4 + a] P [l 3 + 6al 2 – 8a 3 ]/48El5P/8 s3Pl/16 5Pl 3 /384Elwl/12 wl 2 /24 wl 4 /96EIwl/24 wl 2 /96 5wl 4 /4,608EI5wl/96 wl 2 /120 wl 4 /1,743EITABLE 5-2 Maximum Bending Moment, Shear, and Deflection for BeamsDownloaded From : www.EasyEngineering.net
Downloaded From : www.EasyEngineering.netDesign of Wood Members for Formwork 113Many of the equations shown in this table were derived and illustratedin previous sections. The symbols and units were also defined earlier inthis chapter. The span length l and deflection ∆ are measured in inches,and the unit of measure for the uniformly distributed load w is lb per linft. The concentrated load P and shear force V are measured in pounds.Calculating Deflection by SuperpositionTable 5-2 gives equations for various load conditions for calculatingbending stress, shear stress, and deflection. These equations are commonlyused to design wood members for formwork and temporarystructures. However, sometimes there are other load conditions thatmay be applied to the beams shown in Table 5-2. The method ofsuperposition is a technique of determining the total deflection of aww.EasyEngineering.nbeam by superimposing the deflections caused by several simpleloadings. In essence, the total deflection is determined by adding thedeflections caused by several loads acting separately on a beam.The method of superposition is restricted to beams with the samelength and end conditions. Also, this method is restricted to the theoryof small deformations, which means the effect produced by eachload must be independent of that produced by other loads. Each loadmust not cause an excessive change in the original shape or length ofthe beam. Also, the point of maximum deflection caused by the separateloadings must occur at the same location on the beam.The technique of superposition is applicable for combining thetypes of loads shown in Table 5-2. The following examples illustratethe method of superposition for calculating deflection.Example 5-10Use the method of superposition to calculate the total deflection ofthe beam shown below. The single-span beam has four concentratedloads, two 8-lb loads, and two 120-lb loads. A review of Table 5-2shows there is no beam with this load condition. However, Beam 4 inTable 5-2 is a single-span beam with two loads located at a distance afrom each end of the beam. Using Beam 4 in Table 5-2, the deflectiondue to the two 80-lb loads can be calculated and then the deflectiondue to the two 120-lb loads can be calculated. Then, by method ofsuperposition, the two deflections can be added together to obtainthe total deflection due to all four of the loads.Downloaded From : www.EasyEngineering.net
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Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

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