Two wooden members of uniform rectangular cross section are joined using a simple glued scarf splice. The maximum allowable shearing stress and maximum allowable normal stress in the glued splice is 50 MPa and 100 MPa, respectively. The cross-section area of the glued member is 400 mm2. (a) What should the value of the angle  be to achieve maximum load Fmax? (b) What is the magnitude of the maximum load Fmax?

a). α =  26.57  

b). Maximum load is 50 .kN

Explanation:

a).

The normal force is given by

N = σ A cosec β

where, σ is the normal stress

            A is the cross sectional area

Similarly, shear force is given by

S= τ A cosec β

where, τ is the shearing stress

Now from the figure,

tan β = S/N

        = τ/σ

Therefore,  = 63.43

α = 90 - β = 26.57

b).

The normal force is given by

N

We have

∴ N - F sin β = 0

⇒ F = N / sin β

      =

Similarly,

The shear force is given by

S = τ A cosec β

  =

∴ S - F cos β = 0

⇒ F = S / cos β

Therefore, force is 50 kN.

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