3.3Equilibrium conditions and equations of plane generalforce svstemPExamplel Solving constraint reaction force of graphic rigid frame.aSolution: Takethe rigid frame as the researchqbobject, stress as shown in the figure,and establishthe coordinates as shown in the figure.ZX=0: X-qb=0PMaZY=0:Y-P=0XAq6YZm(F)=O: M^-Pa-2xGet the solutionX=qbY=PM, = Pa+-gb2
P A a b q Example1 Solving constraint reaction force of graphic rigid frame. x a b q P A A X YA M A y Solution：Take the rigid frame as the research object, stress as shown in the figure, and establish the coordinates as shown in the figure. X = 0: XA −qb = 0 Y = 0:YA −P = 0 m (F) = 0 : A 0 2 1 2 M A − Pa − qb = XA = qb YA = P 2 2 1 M Pa qb A = + Get the solution： 3.3 Equilibrium conditions and equations of plane general force system
3.3Equilibrium conditions and equations of plane generalforce systemPExample2 calculate the bearing reactionforce of the illustrated beam.mBαASolution: Takethe beam as the researchTTobject, stress as shown in the figure,andTNIestablishthecoordinatesasshownintheabfigure.EPAZX=0:X +Pcosα=0mBαXYAZY=O:Y+Yβ-Psinα=0YBZm(F) = 0:Ypa- Psin α(a+b)-m= 0Get the solution:m+ Pbsin αYA=X=-Pcosαam+ Psin α(a+b)Yβ =a
a b P A m B Example 2 calculate the bearing reaction force of the illustrated beam. Solution：Take the beam as the research object, stress as shown in the figure, and establish the coordinates as shown in the figure. P A m B X A YA YB x y X = 0: XA + Pcos = 0 Y = 0:YA +YB −Psin = 0 mA (F) = 0 :YB a − Psin (a + b) − m = 0 Get the solution： XA = −Pcos a m P a b YB + sin ( + ) = a m Pb YA + sin = − 3.3 Equilibrium conditions and equations of plane general force system
3.3Equilibrium conditions and equations of plane generalforce system0Example3 Solving constraint reaction force of plane rigid frame1b1b1mPSolution: Take the rigid frame as the research object,and the stress is as shown in the figure.aZX=0:X+P=0BNZY=0:Y+R,-Q=0mm0Zm,(F)=0: R,2b-Qb-m- Pa=0Pb1bmGet the solution: XA=-P2aXPa+Qb+mRβ =BA2bY.RsQb- Pa-mY2b
Q A B P m a b b Solution: Take the rigid frame as the research object, and the stress is as shown in the figure. P m a b b A B Q X A YA RB x y ( ) 0 : 2 0 0 : 0 0 : 0 = − − − = = + − = = + = m F R b Qb m Pa Y Y R Q X X P A B A B A Get the solution： b Qb Pa m Y b Pa Qb m R X P A B A 2 2 − − = + + = = − Example3 Solving constraint reaction force of plane rigid frame. 3.3 Equilibrium conditions and equations of plane general force system