Fillet welded joint problems

1. Which lap joint is the more effective, the transverse or the longitudinal, and by how much ?

   [ Transverse, 22% ]

   
   
2. The design normal stress for these welds is 240MPa. Determine the maximum permissible load, F, in each case.     [ 100, 35.3, 14.5, 10.3 kN ]
3. The two beams are each welded to a fixed support as shown. Find the maximum equivalent normal stress in each joint.
   [ 17.5, 104 MPa]
    
4. A force of 7.5 kN acts on the bracket. What is the maximum equivalent normal stress in the fillet ?
   [ 48.0 MPa]
    
    
5. Show that   ∫_L r x ( b x r ) dL = I b ; the symbols being as defined in the above text.
    
6. A straight line extends between the two points [ x₁ y₁ z₁ ]' and [ x₂ y₂ z₂ ]'. Derive the following expressions for the second moments J_xx and I_xy of this line, in terms of the end point coordinates and the line length, L₁₂ :-
       J_xx   =   1/3 L₁₂ ( ( y₁² + y₁ y₂ + y₂² ) + ( z₁² + z₁ z₂ + z₂² ) )
       I_xy   =   1/6 L₁₂ ( 2 ( x₁ y₁ + x₂ y₂ ) + x₁ y₂ + x₂ y₁ )
    
7. The centroidal loading on a circular fillet weld of radius R is F & M. Prove that the local intensity at a point P defined by the angle f on the fillet, is given by the vector shown, where   m = M/R.
    
8. A b x b equal angle is fillet welded orthogonally to a support and loaded by the axial force, F, located at the corner as shown.
   Derive the joint design equation : w b S = 4 n F where n is the safety factor, and S is the strength of the fillet, whose size is w.
    
9. The cantilever, of circular cross-section, is fillet welded to a support using an E48xx rod, and loaded by a force of magnitude F, inclined at [ 4 -3 -12 ]' as shown.
   What is the maximum value of F for a safety factor of 1.5 ?
   [ 19.7 kN]
    
10. The horizontal cantilever of triangular cross-section is fillet welded to a vertical wall and supports a weight of 15 kN as sketched.
    What size of fillet should be laid down if the allowable tensile stress in the joint is 250 MPa? Neglect the fillet not being everywhere right-angled.
    [ 4 mm]
     
     
     
11. The Z-beam is joined obliquely to the plane support by two identical fillet welds, one on each flange, and is loaded by a 1400 Nm couple, M, whose axis is indicated.
    If the design normal stress in the joint is 250 MPa, what size of fillet is necessary?
    [ 6 mm]