Engineering Sciences
2024 · Paper 1
Take it one question at a time. Try an answer, then check your understanding.
Complete GATE XE 2024 Paper 1 overview, original pages and practice · Timed previous-paper practice
Questions 82–84 of 175. Imported answers require review unless explicitly marked reviewed.
Question 82
Open questionXE-DNAT2 marksNeeds review
A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young’s moduli of the two materials are
and
, where
. The beam is subjected to pure bending. If
mm, the distance of the neutral plane from the top surface of the beam is ______ (in mm, rounded off to two decimal places). 
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Open questionXE-DNAT2 marksNeeds review
A stepped beam is made of a material whose Young’s modulus is E. The dimensions of the two stepped sections are such that the sectional moments of inertia,
and
, are related as
. The beam is fixed at one end and a load of F is applied at the free end as shown in the figure. Under this loading condition, if the strain energy of the stepped beam is written as
, then the value of
is ______ (rounded off to two decimal places). 
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Open questionXE-DNAT2 marksNeeds review
A cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figure. The inner diameter of the vessel is 2 m and the length is 10 m. Each row comprises 100 bolts along the length of the vessel. If the vessel is pressurized to a net pressure of
N/m
, and assuming that the end caps of the vessel do not take any load in the radial direction, then the load borne by each bolt is __________ (in kN, rounded off to one decimal place). 
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