㈠ 鍥句腑P銆乹銆乴銆丒I絳夊凡鐭ワ紝鐢ㄧН鍒嗘硶奼傚浘紺烘佷腑鎴闈B鐨勬尃搴﹀拰杞瑙掋
錛1錛夌Н鍒嗘硶錛
璺濆乏絝痻澶勶紝寮鐭╀負錛
0鈮x鈮l/2,M錛坸錛=q(l/2-x)^2/2-P(l-x),
l/2鈮x鈮l錛孧(x)=-P(l-x),
璁捐窛宸︾痻浣嶇疆姊佺殑鎸犲害涓簓錛屽垯
y''=-M(x)/EI,
縐鍒嗗緱錛
0鈮x鈮l/2鏃訛紝y鈥=-錛1/EI錛夆埆[q(l/2-x)^2/2-P(l-x)]dx
=-(1/EI)[(q/3)(l/2-x)^3/(-1)-P/2脳錛坙-x錛塣2/(-1)]+C
=(1/EI)[(q/3)(l/2-x)^3-P/2脳錛坙-x錛塣2]+C
y'灝辨槸姊佺殑杞瑙捨(x),鎵浠ワ細
胃(x)=(1/EI)[(q/3)(l/2-x)^3-P/2脳錛坙-x錛塣2]+C
x=0鏃訛紝胃=0,
鎵浠ワ細
(1/EI)[(q/3)(l/2)^3-P/2脳錛坙錛塣2]+C=0
C=[-ql^3/24+Pl^2/2]/EI
y'=胃(x)=[(q/3)(l/2-x)^3-P/2脳錛坙-x錛塣2-ql^3/24+Pl^2/2]/EI
l/2鈮x鈮l鏃訛細
y'=-錛1/EI錛夆埆[-P(l-x)]dx
=(1/EI)[P/2.(l-x)^2/(-1)+C1]
=(1/EI)[-(P/2)(l-x)^2+C1],
x=l/2鏃訛紝鍓嶉潰涓や釜y'鐩哥瓑錛
-(P/2)(l/2)^2+C1=(q/3)(l/2-l/2)^3-P/2脳錛坙/2錛塣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
鍐嶇Н鍒嗭細
0鈮x鈮l/2:
y=鈭玔(q/3)(l/2-x)^3-P/2脳錛坙-x錛塣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鈮x鈮l錛
y=鈭玔-(P/2)(l-x)^2-ql^3/24+Pl^2/2]/EI.dx
=[錛圥/6錛夛紙l-x)^3-qxl^3/24+Pxl^2/2]/EI+C3,
x=l/2鏃訛紝涓や釜y鐨勫紡瀛愶紝鍊肩浉絳夛細
[-(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=[錛圥/6錛夛紙l/2)^3-ql/2.l^3/24+Pl/2.l^2/2]/EI+C3
[+ql^4/192-Pl^3/6]/EI=C3
鎵浠ワ細
y=[錛圥/6錛夛紙l-x)^3-qxl^3/24+Pxl^2/2+ql^4/192-Pl^3/6]/EI
x=l浠ｅ叆錛
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
錛2錛夎凱鍔犳硶姣旇緝綆鍗曪紝鐢ㄦ偓鑷傛佺殑鍏寮忥紝浠ｅ叆榪鍔犲嵆鍙銆
闇瑕佹敞鎰忕殑鏄錛屽潎甯冭嵎杞介儴鍒嗗彧鏈夊崐璺錛屽彸絝浼稿嚭鐨勮嚜鐢遍儴鍒嗭紝鎸夌洿綰垮勭悊銆
y錛圔錛=y錛坙/2錛+錛坙/2錛.胃錛坙/2錛夛紝
胃錛圔錛=胃錛坙/2錛