Question
Download Solution PDFThe stresses on two perpendicular planes through a point are 60 N/mm2 tension, 40 N/mm2 compression and 30 N/mm2 shear. What is the absolute normal stress on a plane at 60° to that of the tensile stress?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\(σ_1={σ_x+σ_y\over 2}+{σ_x-σ_y\over 2}\,cos2θ+\tau_{xy}\,sin2θ\)
\(σ_2={σ_x+σ_y\over 2}-{σ_x-σ_y\over 2}\,cos2θ-\tau_{xy}\,sin2θ\)
\(\tau_{a-a}=-{σ_x-σ_y\over 2}\,sin2θ+\tau_{xy}\,cos2θ\)
Calculation:
Given
σx = 60 N/mm2
σy = -40 N/mm2
\(\tau_{xy}=30 N/mm^2\)
θ = 60∘
\(σ_1={60+(-40)\over 2}+{60-(-40)\over 2}× cos120^{\circ}+30× sin120^{\circ}\)
σ1 = 10 + 50 × -0.5 + 30 × 0.866 = 10 - 25 + 25.98 = 10.98 N/mm2
σ1 = 10.98 N/mm2
Hence option (1) is the correct answer.
Last updated on Jul 2, 2025
-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10.
-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.
-> UPSC ESE admit card 2025 for the prelims exam has been released.
-> The UPSC IES Prelims 2025 will be held on 8th June 2025.
-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.
-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.