A steel pipe with an outside diameter of 115 mm and an inside diameter of 105 mm supports the loadings shown. Assume a = 470 mm, b = 210 mm, Px = 16 kN, Py = 14 kN, and P₂ = 11 kN. (a) Determine the normal and shear stresses on the top surface of the pipe at point H. (b)Determine the principal stresses and maximum in-plane shear stress magnitude at point H and show the orientation of these stresses on an appropriate sketch. a b
A steel pipe with an outside diameter of 115 mm and an inside diameter of 105 mm supports the loadings shown. Assume a = 470 mm, b = 210 mm, Px = 16 kN, Py = 14 kN, and P₂ = 11 kN. (a) Determine the normal and shear stresses on the top surface of the pipe at point H. (b)Determine the principal stresses and maximum in-plane shear stress magnitude at point H and show the orientation of these stresses on an appropriate sketch. a b
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A steel pipe with an outside diameter of 115 mm and an inside diameter of 105 mm supports the loadings shown.
Assume a = 470 mm, b = 210 mm, Px = 16 kN, Py = 14 kN, and P₂ = 11 kN.
(a) Determine the normal and shear stresses on the top surface of the pipe at point H.
(b)Determine the principal stresses and maximum in-plane shear stress magnitude at point H and show the orientation of these
stresses on an appropriate sketch.
a
P₂
H
(b) On a piece of paper, sketch the x-z stress state and the properly oriented principal stress state. Use the resulting sketch to
answer the questions in subsequent parts of this GO exercise.
(a) The angle -25.86° locates a principal stress plane. Give the stress value including sign if any.
(b) The angle 64.14° locates the other principal stress plane. Give the stress value including sign if any.
(c) What stress or stresses occur on a plane at 19.14°? Give the stress value or values including sign if any.
Answers:
(a) σ= i
MPa,
(b) o =
i
MPa,
(c) σ= i
MPa, T = i
MPa.
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