Strain Energy 277 (b)When used horizontally as a simply supported beam,a concentrated force of 1kN applied at the centre of the support span produces a static deflection of 5mm.The same load will produce a maximum bending stress of 158 MN/m2. Determine the magnitude of the instantaneous stress produced when a mass of 10kg is allowed to fall through a height of 12 mm on to the beam at mid-span. What will be the instantaneous deflection? Solution (a)From eqn.(11.9) 2 252 volume of bar=tr×10s×26=12.76×104 2.6a Then 10×10 σ2×12.76×10-4 0.3+200×10 2×200×109 30+1 g2 109=313×10 and 30×313×102+100x313x102=o Then a2-406.9×103×0-9390×1012=0 406.9×103±√/(166×10°+37560×1012) 0= 2 406.9×103±193.9×106 2 =97.18MN/m2 If the instantaneous deflection is ignored (the term oL/E omitted)in the above calculation a very small difference in stress is noted in the answer, i.e. W(h)=gx volume 2E 100×0.3=g2×12.76×10-4 2×200×109 g2=30×400×109 12.76x10-4=9404×1012 c=96.97MN/m2 This suggests that if the deflection is small in comparison to h(the distance through whichStrain Energy 277 (b) When used horizontally as a simply supported beam, a concentrated force of 1 kN applied at the centre of the support span produces a static deflection of 5 mm. The same load will produce a maximum bending stress of 158 MN/m’. Determine the magnitude of the instantaneous stress produced when a mass of 10 kg is allowed to fall through a height of 12mm on to the beam at mid-span. What will be the instantaneous deflection? Solution (a) From eqn. (11.9) w h +- = - x volume (Fig. 11.7) ( :) ;; 25’ lo6 volume of bar = in x ~ x 2.6 = 12.76 x O’ x 12.76 x Then 10 x 10 1.30 O2 30+- = 109 3i3x 1012 .. 1.30 30 x 313 x 10” f- x 313 x 10” = O’ 109 and Then u2 - 406.9 x lo3 x u - 9390 x 10l2 = 0 406.9 x lo3 f J(166 x lo9 + 37560 x 2 O= 406.9 x lo3 f 193.9 x lo6 2 - = 97.18 MN/m2 If the instantaneous deflection is ignored (the term aL/E omitted) in the above calculation a very small difference in stress is noted in the answer, i.e. O’ x volume 2E W (h) = o2 x 12.76 x lop4 .. 100 x 0.3 = 2 x 200 x 109 30 400 109 .. 02 = = 9404 x 10” 12.76 x .. o = 96.97 MN/mZ This suggests that if the deflection 6 is small in comparison to h (the distance through which