Unwin’s Formula with Example - Riveted Joints, Strength of Materials | Strength of Material Notes - Agricultural Engg - Agricultural Engineering PDF Download

Unwin’s Formula                                                     

Unwin’s formula gives a relation between hole diameter of rivet and thickness of the connected plates. The Unwin’s formula is,

When t > 8mm,  \[d=6\sqrt t\]

When t < 8mm the hole diameter is determined by equating bearing strength and shear strength of the joint as,

\[{\sigma _b}t={\pi\over 4}d{\sigma _s} \Rightarrow d={{4t} \over \pi }{{{\sigma _b}} \over {{\sigma _s}}}\]

In any case d should not be less the thickness (t) of the plate.

Example                                                                           

In a single riveted lap joint, the pitch of the rivet is 100mm, thickness of the plate is 15mm and rivet diameter is 30 mm. Allowable stresses are σ_t = 450 MPa , σ_s = 350MPa and σ_b = 600MPa. Determine the design strength of the joint per pitch length.

Tearing strength,

\[{P_t}={\sigma _t}\left( {b - nd} \right)t\]

Since strength is to be determined per pitch length, b = p and n = 1 . Therefore,

\[{P_t}={\sigma _t}\left({p - d} \right)t=450 \times\left({100-30}\right)\times 15=472.5{\rm{ kN}}\]

Shearing strength,

\[{P_s}={\sigma _s}\left({{\pi\over 4}{d^2}}\right)=350\times {\pi \over 4}\times{30^2}=247.28{\rm{ kN}}\]

Crushing / Bearing strength,

\[{P_b}={\sigma _b}dt = 600 \times 30 \times 15=270{\rm{ kN}}\]

Design strength = min (P_t,P_s,P_b) = 147.2 kN.

Efficiency of the joint \[{\rm{Efficiency }}(\eta )={{{\rm{strength of joint}}} \over {{\sigma _t}pt}}={{{\rm{247}}{\rm{.28}} \times {\rm{1000}}} \over {450 \times 100 \times 15}}=36.63\% \]