. The strength of materials; a text-book for engineers and architects. ansmitted at a and B, the resultant of which isa load of 70 tons acting at d. The following are the properties of the section— A = 28-59 sq. ^^ = 4*45 ^^ = 339 gives z o x = A = 1104° 4 X 5*5 M sin A. = 70 X o D sin A = 70 x e o = 70 x —_ — = 220 in. tons(This is the same as 40 x o b) M cos A. = 70 X o D cos X = - 70 x d e = 70 x v x 2-72 = — 81*6 in. tons(This is the same as 30 x o a) The maximum stress occurs at the top left-hand corner forwhich y = 55, X = — 6 ins. ,,,,., , 220 X 5-5 , 81-6 x 6
. The strength of materials; a text-book for engineers and architects. ansmitted at a and B, the resultant of which isa load of 70 tons acting at d. The following are the properties of the section— A = 28-59 sq. ^^ = 4*45 ^^ = 339 gives z o x = A = 1104° 4 X 5*5 M sin A. = 70 X o D sin A = 70 x e o = 70 x —_ — = 220 in. tons(This is the same as 40 x o b) M cos A. = 70 X o D cos X = - 70 x d e = 70 x v x 2-72 = — 81*6 in. tons(This is the same as 30 x o a) The maximum stress occurs at the top left-hand corner forwhich y = 55, X = — 6 ins. ,,,,., , 220 X 5-5 , 81-6 x 6 . •. Max. bendmg stress = / = 28-59~^^4^2 + 28o9 x 3392 = 214 -f 1-49 = 363 tons per sq. in, 70Direct stress = ^^^^^ = 245 tons per sq. in. .-. combined stress = 608 tons per sq. in. STRESSES IN BEAMS 247 Simplified Result in Special Case.—In the case, as theabove, where the oblique loading is caused by two bendingmoments in the principal axes, M sin X and M cos X will bethe separate bending moments in the two axes and we thusget the following rule—. /0^x3iK^^2//f. Calculate the stresses at any point for each bending momentseparately about the corresponding neutral axes; then the totalstress for the two bending moments will be the sum of the separatestresses. CHAPTER IX DEFLECTIONS OF BEAMS We have found the relation which exists between thestresses in a beam and the bending moment; we now wantto find the relation between the deflections and the bendingmoment. Let c c^ Fig. 121, represent a short length of the centroidline of a beam, the original curvature of which was negligible,and which has become bent to a radius of curvature R. Thisradius R is that which agrees with the very short length c c,and is not the same all along the beam. If the assumptionsthat we previously made with regard to the stresses in beamsstill hold, B r and a e are straight lines after bending, and theymeet at o, the centre of curvature of c c. Draw b f parallelto A E. Now consider the
Size: 1433px × 1743px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyorkdvannostran
