*Bending moment formula = Load*Distance*

bending moment (M) in a beam is a measure of the internal forces that induce a bending effect. It is typically expressed in units of force multiplied by distance (e.g., Newton-meters or pound-feet).

*Sign Convention*

## bending moment formula for Point load

##### End **bending moment**

bending moment at A will be zero because load RA is acting on point A as distance of RA to point A is zero.

Bending moment formula = Load*Distance

load = 6KN

distance = 0

MA = -(6*0) =* *0

bending moment at point B

Bending moment formula = Load*Distance

load RA is 2m away from point B.

load = 6KN

distance = 2m

distance for 9KN load is zero at Point B because it is acting on point B only.

*MB =* *-(6*2)+(9*0) =** *-12KNm

bending moment at point C

MC = -(6*6)+(9*4)+(6*0) =* *0

##### Mid **bending moment**

M(A-B) = -(6*1) = **-6KNm**

*M(B-C) = -(6*4)+(9*2) =** *-6Knm

## bending moment formula for uniformly distributed load (udl)

*In the case of udl load can be calculated by multiplying udl*distance upto which udl is acting*

##### End **bending moment**

MA = -(12*0) = **0**

MB = -(12*6)+(4*6*3) = **0**

##### Mid **bending moment**

M(A-B) = -(12*3)+(4*3*1.5) = **-18KNm**

## uniformly varying load (uvl) – right triangle

*In the case of right triangle load can be calculated by finding the area of triangle = 0.5*b*h*

##### End **bending moment**

MA = (12*0) = **0**

MB = -(6*3)+(0.5*3*12*(3/3)) = **0**

##### Mid **bending moment**

M(A-B) = -(6*1.5)+(0.5*1.5*(12/2)*(1.5/3)) = **-6.75KNm**

## uniformly varying load (uvl) – trapezoidal

*In the case of trapezoidal load can be calculated by finding the area of rectangle + area of triangle = (b*h) + (0.5*b*h)*

##### End **bending moment**

MA = (18*0) = **0**

MB = -(18*6)+(4*6*3)+(0.5*6*6*(6/3)) = **0**

##### Mid **bending moment**

M(A-B) = -(18*3)+(4*3*1.5)+(0.5*3*(6/2)*(3/3)) = **-31.5KNm**

## uniformly varying load (uvl) – isosceles triangle

*In the case of isosceles triangle load can be calculated by finding the area of both right triangle = (0.5*b*h) + (0.5*b*h) *

##### End **bending moment**

MA = (40.5*0) = **0**

MB = -(40.5*9)+(0.5*4.5*18*((4.5/3)+4.5))+(0.5*4.5*18*((2*4.5)/3)) = **0**

##### Mid **bending moment**

M(A-B) = -(40.5*4.5)+(0.5*4.5*18*(4.5/3)) = **-121.5KNm**

## inclined load

##### End **bending moment**

MA = -(3*0) = **0**

MB = -(3*2) = **6KNm**

MC = -(3*5)+(10*sin30*3) = **0**

##### Mid **bending moment**

M(A-B) = -(3*1) = **-3KNm**

M(B-C) = -(3*3.5)+(10sin30*1.5) = **-3KNm**