Determine moment of this normal force - rectangular beam:
A rectangular beam contains a width of 100 mm and a depth of 200 mm. This is utilized as a simply supported beam & the maximum bending stress is restricted to 10 N/mm2. Then determine the following :
(a) Entire normal force on the left bottom corner area of size 40 mm × 60 mm, and
(b) moment of this normal force around the neutral axis.
Solution
Maximum bending stress, σmax = 10 N/mm2
Normal force on the shaded area, left bottom corner is following
![708_Determine moment of this normal force.png](https://www.expertsmind.com/CMSImages/708_Determine%20moment%20of%20this%20normal%20force.png)
= (10/100) × (40 × 60) × (40 + 30)
Here, A = Shaded area = 40 × 60 mm2
= Centroid of shaded area through the neutral axis
= (100 - 60) + ( 60/2) = (40 + 30) = 70 mm
![74_Determine moment of this normal force2.png](https://www.expertsmind.com/CMSImages/74_Determine%20moment%20of%20this%20normal%20force2.png)
Figure
∴ Normal force on the partial beam section is following
= (10/100) × 2400 × 70 = 16800 N = 16.8 N
The partial area is subjected into a tensile force
∴ Normal force on partial beam section = 16.8 kN (tension)
Moment of the force around the neutral axis
= (σmax / ymax) × Is
Is = Moment of inertial of the shaded area around the neutral axis
= (1/12) × 40 × (60)3 + (40 × 60) × (70)2 = 1248 × 104 mm4
∴ Moment of normal force around the neutral axis
= ( 10 /100) × 1248 × 104 = 1248 × 103 Nm = 1248 m