By C. B. Smith, N. Hiller and G. E. Walker (Auth.)
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Extra resources for Applied Mechanics for Engineers
ED = -DA sin 60° = - ( v- 4 - 3 7 5 ) ^ 7 = - 5 - 0 5 tonf Ό-866 , . Λ (compressive). AE cos0° + ED cos 60° + DA cos 270° = 0. ·. AE = —ED — = - ( -v5 - 0 5 ) } — = 2-525 tonf cos0° 1-0 u · \ (tension). DE sin 240°+ EF sin 300° + FD sin 330° = 0. '. ( - 5 - 0 5 ) ( - 0 - 8 6 6 ) + £ F ( - 0 - 8 6 6 ) + F i ) ( - 0 - 5 ) = 0. ·. 4-375-0-866 EF-0 5 FD = 0. (1) DE cos 240° + £ F c o s 300°+FD cos 330° = 0. ·. ( - 5 - 0 5 ) (-0-5)+ EF( + 0-5)+ FD (0-866) = 0. ·. 2-525 + 0-5 EF+ 0-866 FD = 0. ). CG sin 150°+ GB sin 180° + £ C sin 270° = 0.
Taking moments about support (1) where the reaction Rx acts, 16 R2 = 2 4 x - | ( 1 2 - 3 ) = 108 tonf ft. Λ R2 = 108/16 = 6-75 tonf. Taking moments about support (2) where the reaction R2 acts, 16 Rt = 24 χ \ ( 1 2 - 5 ) = 84 tonf ft. ·. R, = 84/16 = 5-25 tonf. Checking results, R1+R2 = 5-25 + 6-75 = 12 tonf = total load. Cantilever Beam In the case of a cantilever beam the reaction at the fixed or built-in end must provide not only a force to balance the external loads on the beam, but also a fixing moment to balance the moments of those forces about the point of support.
3, what will be the shear stress in the rivets and the maximum tensile stress in the plates ? Assuming that the 3 tonf load is equally divided b etween the three rivets, shear force on each rivet = 1 tonf. 1 t o n f ^, >> shear stress in rivets = - . 0 = 5-1 tonf in . 2 2 l J £πχ(|) ιη STRESS AND STRAIN 55 For section XX, total load = 3 tonf and cross-sectional area of 2 plate in tension = i ( 3 —|) = | i n . maximum W 3 1 tensile stress in plates = — = - = 4-8 tonf fin . A ¥r Direct Strain When a material is subject to an external load which sets u p a tensile or compressive stress in the material, the stress is accompanied by a change in length in the direction of the stress and this change in length per unit length is known as strain.