The built-up beam is formed by welding together the thin plates of thickness 5 mm. determine the location of the shear center o.

The location of the shear center o is 0.033 or 33 m

Explanation:

Solution

Recall that,

The moment of inertia of the section is =  I = 0.05 * 0.4 ^3 /12 + 0.005 * 0.2 ^3/12

= 30 * 10 ^ ⁻⁶ m⁴

Now,

The first moment of inertia is

Q =ῩA = [ (0.1 -x) + x/2] (0.005 * x)

= 0.5x * 10 ^⁻³ - 2.5 x * 10⁻³ x²

Thus,

The shear flow is,

q =  VQ/I

so,

P =  (0.5x * 10 ^⁻³ - 2.5 x * 10⁻³ x²)/ 30 * 10 ^⁻⁶

P = (16.67 x - 83. 33  x²)

The shear force resisted by the shorter web becomes

Vw,₂ = 2∫ = ₀.₁ and ₀ = P (16.67 x - 83. 33  x²) dx = 0.11x

Then,

We take the moment at a point A

∑Mₐ = 0

- ( p * e)- (Vw₂ * 0.3 ) = 0

e =  0.11 p * 0.3/p

which gives us 0.033 m

= 33 m

Therefore the location of the shear center o is 0.033 or 33 m

Note: Kindly find an attached diagram to the question given above as part of the explanation solved with it.