㈠ 锲句腑P銆乹銆乴銆丒I绛夊凡鐭ワ纴鐢ㄧН鍒嗘硶姹傚浘绀烘佷腑鎴闱B镄勬尃搴﹀拰杞瑙掋
锛1锛夌Н鍒嗘硶锛
璺濆乏绔痻澶勶纴寮鐭╀负锛
0铌x铌l/2,M锛坸锛=q(l/2-x)^2/2-P(l-x),
l/2铌x铌l锛孧(x)=-P(l-x),
璁捐窛宸︾痻浣岖疆姊佺殑鎸犲害涓簓锛屽垯
y''=-M(x)/EI,
绉鍒嗗缑锛
0铌x铌l/2镞讹纴y钬=-锛1/EI锛夆埆[q(l/2-x)^2/2-P(l-x)]dx
=-(1/EI)[(q/3)(l/2-x)^3/(-1)-P/2脳锛坙-x锛塣2/(-1)]+C
=(1/EI)[(q/3)(l/2-x)^3-P/2脳锛坙-x锛塣2]+C
y'灏辨槸姊佺殑杞瑙捨(x),镓浠ワ细
胃(x)=(1/EI)[(q/3)(l/2-x)^3-P/2脳锛坙-x锛塣2]+C
x=0镞讹纴胃=0,
镓浠ワ细
(1/EI)[(q/3)(l/2)^3-P/2脳锛坙锛塣2]+C=0
C=[-ql^3/24+Pl^2/2]/EI
y'=胃(x)=[(q/3)(l/2-x)^3-P/2脳锛坙-x锛塣2-ql^3/24+Pl^2/2]/EI
l/2铌x铌l镞讹细
y'=-锛1/EI锛夆埆[-P(l-x)]dx
=(1/EI)[P/2.(l-x)^2/(-1)+C1]
=(1/EI)[-(P/2)(l-x)^2+C1],
x=l/2镞讹纴鍓嶉溃涓や釜y'鐩哥瓑锛
-(P/2)(l/2)^2+C1=(q/3)(l/2-l/2)^3-P/2脳锛坙/2锛塣2-ql^3/24+Pl^2/2
-Pl^2/8+C1=-Pl^2/8-ql^3/24+Pl^2/2
C1=-ql^3/24+Pl^2/2
y'=胃(x)=[-(P/2)(l-x)^2-ql^3/24+Pl^2/2]/EI
鍐岖Н鍒嗭细
0铌x铌l/2:
y=鈭玔(q/3)(l/2-x)^3-P/2脳锛坙-x锛塣2-ql^3/24+Pl^2/2]/EI.dx
=[-(q/12)(l/2-x)^4+(P/6)(l-x)^3-qxl^3/24+Pxl^2/2]/EI+C2,
x=0,y=0:
[-(q/12)(l/2)^4+(P/6)(l)^3]/EI+C2=0
C2=[ql^4/192-Pl^3/6]/EI
y=[-(q/12)(l/2-x)^4+(P/6)(l-x)^3-qxl^3/24+Pxl^2/2+ql^4/192-Pl^3/6]/EI
l/2铌x铌l锛
y=鈭玔-(P/2)(l-x)^2-ql^3/24+Pl^2/2]/EI.dx
=[锛圥/6锛夛纸l-x)^3-qxl^3/24+Pxl^2/2]/EI+C3,
x=l/2镞讹纴涓や釜y镄勫纺瀛愶纴鍊肩浉绛夛细
[-(q/12)(l/2-l/2)^4+(P/6)(l/2)^3-ql/2.l^3/24+Pl/2.l^2/2+ql^4/192-Pl^3/6]/EI=[锛圥/6锛夛纸l/2)^3-ql/2.l^3/24+Pl/2.l^2/2]/EI+C3
[+ql^4/192-Pl^3/6]/EI=C3
镓浠ワ细
y=[锛圥/6锛夛纸l-x)^3-qxl^3/24+Pxl^2/2+ql^4/192-Pl^3/6]/EI
x=l浠ｅ叆锛
yB=[-ql^4/24+Pl^3/2+ql^4/192-Pl^3/6]/EI
=[-7ql^4/192+Pl^3/3]/EI
胃B=[-ql^3/24+Pl^2/2]/EI
锛2锛夎凯锷犳硶姣旇缉绠鍗曪纴鐢ㄦ偓镊傛佺殑鍏寮忥纴浠ｅ叆杩锷犲嵆鍙銆
闇瑕佹敞镒忕殑鏄锛屽潎甯冭嵎杞介儴鍒嗗彧链夊崐璺锛屽彸绔浼稿嚭镄勮嚜鐢遍儴鍒嗭纴鎸夌洿绾垮勭悊銆
y锛圔锛=y锛坙/2锛+锛坙/2锛.胃锛坙/2锛夛纴
胃锛圔锛=胃锛坙/2锛