find shear force and bending moment diagram of inclined load manual vs staad pro

figure

draw shear force and bending moment diagram of given figure. 

SIGN CONVENTION 

STEPS FOR FINDING REACTIONS

Here, In The Above Figure We Have Two Unknown Reaction Force RA And RC.

To Solve Two Unknowns We Need Two Equations.

1.   Apply First Equilibrium Equation

∑FY( Summation Of Vertical Forces)= 0

Here, TWO Vertical Reaction Forces Are Acting Upward. They Are +RA And +RC and One Inclined load is acting downward and the angle inclination is 30 degree.

Divide the inclined load into two components.

Horizontal force= 5cos30 and vertical force= 5sin30.     

Take The Summation Of All Vertical Forces Acting On The Beam (Both Upward And Downward)

In the inclined load case, we have to find Horizontal force (FX) also

Take The Summation Of Horizontal Force Acting On The Beam (Both left And right).

Force acting towards right is taken as positive (+) and force acting towards left is taken as negative (-).

2.   Apply Second Equilibrium Equation

∑M(Summation Of Moments)= 0

Formula Of Moment= Force*Distance.

e.g. ∑MB= +(RA*1)= RA

Here We Have Taken ∑M At B.

Take The Summation Of All Moments Acting On The Beam (Both Clock Wise And Anti clock Wise)

(Better See The Sign Convention For Positive And Negative Moment Or Clockwise And Anticlockwise Moment).

By Solving The Two Equations We Can Calculate Both The Support Reaction.

Once We Got The Values Of Reaction We Can Calculate Shear Force And Bending Moment.

FINDING THE REACTION

Vertical Reaction

∑FY=0

RA-5SIN30+RC=0

RA+RC= 2.5KN – (1)

∑MA=0

(RA*0)+(5SIN30*1)-(RC*3)=0

RC=5SIN30/3= 0.83KN

 FROM EQN (1)

RA+RC=2.5KN

RA=2.5-.83=1.667KN

Horizontal Reaction

∑FX=0

RAX-5COS3=0

RAX=4.330KN

To Calculate The End Shear Force

 Take summation of forces acting on node or member.

In the below calculation L indicates left and R indicates right.

CALCULATION OF END SHEAR FORCE

FA=RA=1.667KN

FB=1.667-5SIN30=-0.883KN

RC=1.667-5SIN30+0.883=0

To Calculate The Mid Shear Force

 Take Summation of forces acting at the mid span of the member.

CALCULATION OF MID SHEAR FORCE

F(A-B)= 1.667KN

F(B-C)= 1.667-5SIN30= -0.833KN

To Calculate The End Bending Moment

 Calculate moments acting at the mid span of the member and add the remaining distance up to which node/member you want to calculate the moment.

CALCULATION OF END BENDING MOMENTS

MA=(1.667*0)=0

MB=(1.667*1)= 1.667KNm

MC=(1.667*3)-(5SIN30*2)=0

To Calculate The Mid Bending Moment

 Calculate moments acting at the mid span of the member and add the remaining distance up to which node/member you want to calculate the moment.

CALCULATION OF MID BENDING MOMENTS

M(A-B)= (1.667*0.5)= 0.833KNm

M(B-C)= (1.667*2)-(5SIN30*1)= 0.833KNm

To Calculate The Axial Force

 Take summation of forces acting on node or member.

CALCULATION OF Axial Force

FA= RAX= 4.33KN

FB=4.33-5COS3=0

shear force and bending moment diagram manually
shear force and bending moment diagram manually
software output

shear force

bending moment

axial force

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