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### Stress Angled Strut - Supporting Pin Equations and Calculator

Bearing Stress Between Angled Strut and Supporting Pin Equations and Calculator

Figure 1
(a) Pin connection between strut S and base plate B. (b) Cross section through the strut S

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The average value of the bearing stress between the strut and the pin is found by dividing the force in the strut by the total bearing area of the strut against the pin. The latter is equal to twice the thickness of the strut (because bearing occurs at two locations) times the diameter of the pin (see figure (b)). Thus, the bearing stress is:

Equation 1
σb1 = P / ( 2 t dpin )

Shear stress in pin. As can be seen from figure (b), the pin tends to shear on two planes, namely, the planes between the strut and the gussets. Therefore, the average shear stress in the pin (which is in double shear) is equal to the total load applied to the pin divided by twice its cross-sectional area:

Equation 2
τpin = P / ( 2 π dpin2 / 4 )

(3) Bearing stress between pin and gussets. The pin bears against the gussets at two locations, so the bearing area is twice the thickness of the gussets times the pin diameter; thus:

Equation 3
σb2 = P / ( 2 tG dpin )

(4) Bearing stress between anchor bolts and base plate. The vertical component of the force P (see figure (a)) is transmitted to the pier by direct bearing between the base plate and the pier. The horizontal component, however, is transmitted through the anchor bolts. The average bearing stress between the base plate and the anchor bolts is equal to the horizontal component of the force P divided by the bearing area of four bolts. The bearing area for one bolt is equal to the thickness of the plate times the bolt diameter. Consequently, the bearing stress is:

Equation 3
σb3 = P cos θ / ( 4 tB dbolt )

(5) Shear stress in anchor bolts. The average shear stress in the anchor bolts is equal to the horizontal component of the force P divided by the total cross-sectional area of four bolts (note that each bolt is in single shear). Therefore:

τbolt = P / ( 2 π dpin2 / 4 )

Note. Any friction between the base plate and the mounting surface would reduce the load on the anchor bolts.

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References:

Stress-Strain State at a Point of Elastic Deformable Solid, 2010
Editor-in-Chief
Yakiv Karpov
Ministry of Education and Science Ukraine