The steel structure (E=200GPA) shown in Figure Q4, is consisted of the solid bar, DC (length, L of 500mm and a round cross section of 35 mm diameter) and a hollo shaft, AD. (Length, b of 400mm, outer diameter, d of 40mm and inner diameter of 20 mm). Both components are attached to a rigid disc at D, are positioned in the horizontal plane xz, and are perpendicular to each other (along z and x axes as shown in Figure. Q4). The solid bar is loaded in two directions at free end, C as shown with values of P=2kN and F=3kN. The hollow shaft AD is built-in (fixed) into the wall (note points A and B on the outer surface of the shaft on top and front sides where A is on the y axis and B is on the z axis).
The steel structure (E=200GPA) shown in Figure Q4, is consisted of the solid bar, DC (length, L of 500mm and a round cross section of 35 mm diameter) and a hollo shaft, AD. (Length, b of 400mm, outer diameter, d of 40mm and inner diameter of 20 mm). Both components are attached to a rigid disc at D, are positioned in the horizontal plane xz, and are perpendicular to each other (along z and x axes as shown in Figure. Q4). The solid bar is loaded in two directions at free end, C as shown with values of P=2kN and F=3kN. The hollow shaft AD is built-in (fixed) into the wall (note points A and B on the outer surface of the shaft on top and front sides where A is on the y axis and B is on the z axis).
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.3.28P: A T-frame structure is torn posed of a prismatic beam ABC and a nonprismatic column DBF. The beam...
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![The steel structure (E=200GPa) shown in Figure Q4, is consisted of the solid bar, DC (length, L
of 500mm and a round cross section of 35 mm diameter) and a hollo shaft, AD. (Length, b of
400mm, outer diameter, d of 40mm and inner diameter of 20 mm). Both components are attached
to a rigid disc at D, are positioned in the horizontal plane xz, and are perpendicular to each other
(along z and x axes as shown in Figure. Q4). The solid bar is loaded in two directions at free
end, C as shown with values of P=2kN and F=3kN. The hollow shaft AD is built-in (fixed) into the
wall (note points A and B on the outer surface of the shaft on top and front sides where A is on
the y axis and B is on the z axis).
D
F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29e65c26-0725-44c0-a25a-917c4b63231a%2F668e0bc3-aeb0-4d52-a9ab-b54abda3ce15%2Ftbtq6xm_processed.png&w=3840&q=75)
Transcribed Image Text:The steel structure (E=200GPa) shown in Figure Q4, is consisted of the solid bar, DC (length, L
of 500mm and a round cross section of 35 mm diameter) and a hollo shaft, AD. (Length, b of
400mm, outer diameter, d of 40mm and inner diameter of 20 mm). Both components are attached
to a rigid disc at D, are positioned in the horizontal plane xz, and are perpendicular to each other
(along z and x axes as shown in Figure. Q4). The solid bar is loaded in two directions at free
end, C as shown with values of P=2kN and F=3kN. The hollow shaft AD is built-in (fixed) into the
wall (note points A and B on the outer surface of the shaft on top and front sides where A is on
the y axis and B is on the z axis).
D
F
![Answer the following questions:
a) Without detailed stress calculations, can you identify which of the two points A and B is
more highly stressed (clearly justify your answer)?
b) Ignoring the direct shear stress due to shear forces all over the structure, Identify and
show the values and senses (directions) of all loading effects (forces and moments)
acting on the wall section of shaft (view section at the wall in -x direction) as well as on
the joint end of the solid bar (view section at disc joint, D in the -z direction).
c) Based on the findings of part b. above, identify (show) the weakest point on the section
at the wall (Built in end). Is it A or B or somewhere else? Then work out the stress state
at the weakest point on the wall section.
d) Calculate principal stress state for the weakest point. Then calculate von-Mises
stress and use von-Mises failure theory considering a safety factor of 1.5, to find
the minimum Yield strength of the material required for fabrication of the shaft.
Check if for this material the solid bar is also safe!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29e65c26-0725-44c0-a25a-917c4b63231a%2F668e0bc3-aeb0-4d52-a9ab-b54abda3ce15%2F0eyvtos_processed.png&w=3840&q=75)
Transcribed Image Text:Answer the following questions:
a) Without detailed stress calculations, can you identify which of the two points A and B is
more highly stressed (clearly justify your answer)?
b) Ignoring the direct shear stress due to shear forces all over the structure, Identify and
show the values and senses (directions) of all loading effects (forces and moments)
acting on the wall section of shaft (view section at the wall in -x direction) as well as on
the joint end of the solid bar (view section at disc joint, D in the -z direction).
c) Based on the findings of part b. above, identify (show) the weakest point on the section
at the wall (Built in end). Is it A or B or somewhere else? Then work out the stress state
at the weakest point on the wall section.
d) Calculate principal stress state for the weakest point. Then calculate von-Mises
stress and use von-Mises failure theory considering a safety factor of 1.5, to find
the minimum Yield strength of the material required for fabrication of the shaft.
Check if for this material the solid bar is also safe!
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