A rectangular piece of material is subjected to tensile stresses of 83 and 65 N/mm² on mutually perpendicular faces. Find the strain in the direction of each stress and in the direction perpendicular to both stresses. Determine also the maximum shear strain in the plane of the stresses, the maximum shear stress and their directions. Take E=200 000 N/mm² and v=0.3. Ans. 3.18×10¬ª, 2.01×10-4, –2.22×10-4, 7 max=1.17×10-“, Tmax=9.0 N/mm² at 45° to the direction of the given stresses.

A rectangular piece of material is subjected to tensile stresses of 83 and 65 N/mm² on mutually perpendicular faces. Find the strain in the direction of each stress and in the direction perpendicular to both stresses. Determine also the maximum shear strain in the plane of the stresses, the maximum shear stress and their directions. Take E=200 000 N/mm² and v=0.3. Ans. 3.18×10¬ª, 2.01×10-4, –2.22×10-4, 7 max=1.17×10-“, Tmax=9.0 N/mm² at 45° to the direction of the given stresses.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: answers are in the botom

A: If you have any doubts please comment

Q: A rod having a circular cross section (radius; 0.5 in, height; 15 in) is subjected to loadings as in…

A: torque at fixed end T=540 lb.indiameter of shaft d=0.5 inthen shear stress at A abd B…

Q: 5 - An aluminum circular shaft, fixed at both ends, is loaded by torques applied at points B and C,…

A: Given Data Shear modulus (G) = 85 GPa Diameter of shaft (d) = 40mm Length of AB (LAB) = 0.5m =…

Q: The stresses shown act at a point in a stressed body. Normal and shear stress magnitudes acting on…

Q: The stresses shown act at a point on the free surface of a machine component. Normal and shear…

A: The given data is shown below: Sx=12.4 ksiSy=3.5 ksiSxy=3.6 ksiβ=29°

Q: The stresses shown act at a point on the free surface of a machine component. Normal and shear…

A: Using transformation equation

Q: The beam shown is subjected to two loads, one point and the other uniformly distributed. Determine…

Q: (2) A square member (400mm x 400mm) sustains an internal shear force of 150 kN and an internal…

A: Given: A square cross section of 400mm × 400mm Shear force = 150KN Bending moment = 250KN-m…

Q: A beam having the cross section shown is subjected to a couple that acts in a horizontal plane.…

A: z = 1.43 in ( from left side )z = 5 - 1.43 = 3.57 in ( from right side )Iy = 11.3 in4Maximum…

Q: A square steel bar of dimension 50 mm x 50 mm x 150 mm is subjected to an axial load of 250 kN.…

Q: The differential element above represents the state of plane stress at a pont J steel beam. Which of…

A: Given data: σX=60 ksiσY=-20 ksiζXY=40 ksi

Q: A cube of material (E 15,000 psi, v 0.25) of side length 2" is shown in the x, y plane. Take x…

A: Change in length of the cube depends on the length of the sides of the cube and the normal stress…

Concept explainers

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

A rectangular piece of material is subjected to tensile stresses of 83 and 65 N/mm on mutually
perpendicular faces. Find the strain in the direction of each stress and in the direction
perpendicular to both stresses. Determine also the maximum shear strain in the plane of the
stresses, the maximum shear stress and their directions. Take E=200 000 N/mm² and v=0.3.
Ans. 3.18×10 4, 2.01×10-4, –2.22×10-4, 7max=1.17x10-4, Tmax=9.0 N/mm² at 45° to the
direction of the given stresses.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length R. It is subjected to a distributed torque of intensity z per unit distance. The intensity varies linearly from z = 0 at the free end to a maximum value z = zo at the support. Express your answer in terms of maximum value zo , length R, shear modulus G and polar moment of inertia Ip . U =
Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown. If 0 = 44 MPa in the direction shown, determine the principal stresses at the point. 85 MPa 56 MPa O 70.9 MPa and -97.0 MPa 82.8 MPa and -136.0 MPa 89.5 MPa and -64.2 MPa 75.1 MPa and -124.1 MPa 64.9 MPa and -105.9 MPa
A beam of rectangular cross-section 40 x 20 mm is loaded with tensile force 1000 N as shown in figure. A B BO Calculate the shear stress on oblique plane at 0 = 45° A 0.625 MPa C 0.31 MPa F D 1.25 MPa
Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown. Let T = 39 MPa and o = 19 MPa. Determine the center ocenter of the corresponding in- plane Mohr's circle. 50 MPa -21.56 MPa O -17.85 MPa O -10.87 MPa -14.07 MPa -15.50 MPa
The stresses shown in the figure act at a point on the free surface of a machine component. If o = 22.4 ksi in the direction shown, determine the shear stress Txy at the point. Txy O 14.48 ksi 11.51 ksi O 13.53 ksi O 10.63 ksi O 8.84 ksi 5.0 ksi 24° 2.8 ksi
A cube of side 100 mm is subjected to an axial compressive load of 200 kN. Its lateral strain is prevented by applying uniform pressure but only one fourth of lateral strain could be prevented, then which of the following statements is/are correct? Assume E = 200 MPa and μ = 0.3. A The decrease in length in direction of load after applying pressure is 9.358 x 10-3 mm. B The uniform pressure applied has a value of 8.57 N/mm². C The uniform pressure applied has a value of 2.14 N/mm². D The increase in length in lateral direction after applying pressure is 2.25 x 10-³ mm.
Calculate the design moment strength Mu for the following section. Take f'c = 40 MPa. Sketch the strain and stress distribution diagrams for each section and try to work out your solutions using equilibrium conditions. Yield stress for N bars is 500 MPa. 75 700 60 1500 T 4N28 450