Combined Loadings

Thin-Walled Pressure Vessels

Cylindrical Pressure Vessel Spherical Pressure Vessel

What is Thin?

Spherical Pressure Vessels

Guidelines for Determining the Stress State caused by Combined Loadings

Internal Loading

– find internal normal & shear forces and bending and torsional moments – forces act through centroid & moments about centroidal axes

Average Normal Stress

– compute stress associated with each internal load – represent stress acting an element or distribution over cross section

Normal Force

– internal normal force due to uniform stress distribution

Shear Force

– internal shear force in a member subjected to bending is due to a shear-stress distribution determined from the shear formula

Bending Moment

– for straight members, internal bending moment is due to a normal stress distribution determined from the flexure formula

Torsional Moment

– for circular shafts and tubes, the torque is due to a shear stress distribution determined from the torsional formula

Thin-Walled Pressure Vessels

– for cylindrical vessels, the internal pressure causes a biaxial state of stress with hoop and circumferential components

– for spherical vessels, the biaxial state of stress is represented by two equivalent components

Superposition

– use principle of superposition to determine the resultant normal and shear stress components

– show resultants on an element of material located at the point, or show results as a distribution of stress acting over the member’s cross-sectional area

Guidelines for Determining the Stress State caused by Combined Loadings - continued

8-43 Known: The uniform sign is supported by the pipe AB, and is subjected a uniform wind pressure.Find: Determine the state of stress at points C and D. Show the results on a differential volume element located at each of these points.Data: The sign weighs 1500 lb. Pipe AB has an inner radius of 2.75 in. and an outer radius of 3.00 in. The uniform wind pressure p = 150 lb/ft2.Assumptions: Neglect the thickness of the sign, and assume that it is supported along the outside edge of the pipe.