Chapter 5 Member Forces in Beams (梁) and Frames 同大学 土工程学院 TONGI UNIVERSITY COLLGE OF CVI ENGINEERING 5.2 internal forces() for flexural (受弯)members M M C V RA x R X RB RA Mv M T/C: the axial force M M V: the shear force 单 M: the bending moment C V M M 月济大学。 2 TONGJI UNIVERSITY
5.3 notation(符号)and sign convention(符号规定) +M +M +7 Section +M +M wt☐ Element 同橋大学 土亦工程学院 5.5 determination of internal forces (内力) 卜4 4 kips P=4 kips w=2 kips/ft V M B x- 8 (b) (a) 2x3-6) x-6 R=2x2 2 4 kips /2 2 kips/ft 4 kips M 2 kips/ft M B 6' -6* 6 X3 (c) (d)
5.6 relationships between load(荷载) shear(剪力)，and bending moment(弯矩) ww(x) p·△x ·△x k0≤入≤1) 下 p+△p p(x)=p ●A B● V(x)=V dx 0 M(x)=.M M+△M (a) y+△ V+(pa·△)-(V+△=0 AV M+(V.△x)+(Pp。·△xA·△x)-(M+△M)=0 △M △x =V+(p。λ△) dv =p M=v 同像大学 士本工期 5.6 continued V+dV g dv △VA-B =p d dv=pdx dx V=[pdx+C d'M Va-Vi=AV-2=pdx MB MA MM+dM dM=V △MA-B dx dM=Vdx d M=vdx+C2 M2-M,=△M-2=Vd 1+M 学国 土本工程学院 6
5.7 shear and moment diagrams R=24 kips 19595.0690 6 w=2 kips/ft P=13.5 kips 72 moment (kip-ft) (c) RA=19.5 kips Rg=18 kips -12' 44' (d) R=2x (a) w =2 kips/ft 19.5 V=0 (-5.06) (95.06) (-18) shear (kips) -x=9.75' -45 （-72) 2.25 -18 RA 19.5 kips (b) (e) 5.7 example 2 3 k/ft d R2、=10 10 1R、=5 V=∫pdk+C=∫0.3x-3)k+C ,M=vk+G=∫o152-3x+10k+G2 态ne=o-0 1Rgy=10* +10 19.24 V=0.15x2-3r+10 M=0.05r3-1.5r2+10x V(k) 4.23
5.8 qualitative(定性)deflected (挠曲) structures 27kips M=148 kip-ft 10 kips hinge w=9 kips/ft D C RA=20.8 kips Rc=70.2 kips 4.8' 20.8 kips 27 kips 10.8 kips shear (kips) 1.2 -43.2 kips (b) 5.8 continued 49.68 1.48 moment (kip-ft) -64.8 -54 -148 (c) 909 0- hinge point of inflection (d) 同©大学 目 土本工程学院 10