RIVETED JOINTS FOR CONSTRUCTION OF BOILERS The best knowledge of the strength and proportions of riveted joints can be obtained by tests of full sized pieces. Let us consider the strength and efficiency mathematically. Riveted joints may fail in several ways. 1. By shearing the rivets. 2. By tearing the plate at the reduced section between the rivets. 3. By crushing the plate or rivets where they are in contact. 4. By cracking the plate between the rivet hole and the edge of the plate. As the lap in practice can always be made sufficiently wide a joint need never fail in this last way.
As all stresses may be resolved into the three kinds, tensile, compressive and shearing, we will investigate for these stresses. Let P = the tensile stress transmitted from one plate to the other by a single rivet, t = the thickness of the plate, d = the diameter of the rivet, p = the pitch, and St Ss and Sc the unit stresses in tension, shear and compression respectively produced by P on the plates and rivets. Therefore the tension on the plate, P will be equal to the area of the metal between the rivets multiplied by its unit tensile stress, or P = t (p — d) St For shear, P will equal the area of the rivet multiplied by the unit shearing stress, or P = For compression, the stress is supposed to be equivalent to a stress uniformly distributed over the projection of the cylindrical surface on a plane through the axis of the rivet. Then P will be equal to the area of the projection multiplied by the unit compressive stress, or P = tdSc The above formulas are for single riveted lap joints. If another row of rivets is used the plates should have a wider lap. Let p = the pitch in one row; then the stress will be distributed over two rivets.
The three formulas in this case will be.
P t (p — d) St P = 2 tdSc For single riveted butt joint, the shear comes on two rivets; this is called double shear. The above formulas become P = t (p —d) St P=2*(1/4)*pi*d*d*Ss P = tdSc The efficiency of a joint is the ratio of its allowable stress to the allowable stress of the uncut plate. The allowable stress of
the plate is represented by the formula Then the for tension is, E = (t(p - d)St)/(ptSt) = (p - d)/p For shear, E = (1/4*pi*d*d*Ss)/(p*t*St) or (1/4*pi*d*d*Ss*c)/p*t*St) For compression, E = (tdSc)/(ptSt) or dSc/pSt or dSca/pSt In the above formulas, a = the number of rivets in the width p, and c = the number of rivet sections in the same space. The smallest value of E is to be taken as the efficiency of the joint.
In designing, we try to get a joint in which all parts will have equal strength or the resistance of the plate to tension will equal the resistance of the rivets to shearing and each will equal the resistance of the rivet to compression or crushing. This will be the case if the three efficiencies are equal.
Solving for d in the second and third we get (1/4*pi*d*d*Ss*c)/(p*t*St) = (d*Sc*a)/(p*St) or d = (4*a*Sc*t)/(pi*c*Ss)If we know t we can find d from the above equation.
To find the pitch we make the first equation equal to the third, or the formula for tension equal that of compression, and solve for p (p-d)/p = (dSca)/PSt , p = d(Sca/St +1) substituting the value for d, obtained above, p = ((4aSct)/(pi*cSs))*(Sc*a/St + 1) To get the formula for efficiency we insert these values for d and p, in any of the formulas for efficiency already obtained.
A good joint can be designed without these formulas (in fact they serve as a guide only), if attention is paid to the rules deduced from tests and conforming to 'good practice by experienced engineers and boiler makers. In designing a riveted joint, good practice favors the following : The pitch of rivets, for single riveting, should be about 2-1/2 times the diameter of the rivets and for double riveting about 3-3/4 times the diameter.
The pitch near a calked edge must not be too great for proper calking.
Rivets must not be too near together.
The lap, or the distance from the centre of the rivet to the edge of the over-lapping plate should be at least 1 times the diameter of the rivet.