Combined Stress Analysis: Connection Design

The Concept: Failure Modes

A single load creates multiple potential failure paths. A safe design must prevent all of them.

1. Plate Tension

$\sigma_t = \frac{P}{(w-d)t}$

Failure: Plate tears at the hole section.

2. Bolt Shear

$\tau_{bolt} = \frac{P}{A_{circle}}$

Failure: Bolt is sliced in half.

3. Bearing

$\sigma_b = \frac{P}{dt}$

Failure: Material crushes at contact.

4. Plate Shear (Tear-out)

$\tau_{plate} = \frac{P}{2et}$

Failure: Bolt rips out the end of the plate.

Comprehensive Examples

1. Single Bolted Lap Joint

Two steel plates are joined by a single 20 mm diameter bolt. The plates are 120 mm wide and 12 mm thick. The joint transmits a load of 60 kN. The end distance is 40 mm. Calculate all stresses.

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2. Clevis Joint (Fork & Eye)

A clevis joint supports a load of 100 kN. The pin diameter is 30 mm. The single "eye" plate is 20 mm thick. The two "fork" plates are each 12 mm thick. Calculate the Shear stress in the pin and the Bearing stress in the eye.

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3. End Post Truss Connection

A tie rod in a truss carries a pull of 80 kN. It is connected by a 25 mm diameter bolt. The width of the rod is 100 mm. Determine the required thickness ( $t$ ) of the rod if the allowable bearing stress is 200 MPa and allowable tensile stress is 120 MPa.

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