1. Combined Loadings Thin-Walled Pressure Vessels Cylindrical Pressure VesselSpherical Pressure Vessel

2. What is Thin?

5. Spherical Pressure Vessels

6. 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

7. 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. 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/ft 2. Assumptions: Neglect the thickness of the sign, and assume that it is supported along the outside edge of the pipe.