7-82. The material distorts into the dashed positionshown. Determine the average normal strains along thediagonals AD and CF.15 mm30 mm50 mm200 mm50 mm-150mm|F

Answered: 7-82. The material distorts into the…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A plane element removed from a thin-walled cylindrical shell loaded in torsion is subject to the shearing stresses shown in Fig. 3-20. Determine the principal stresses existing in this element and the directions of the planes on which they occur. Ans. 50 MPa at 45° 50 MPa 50 MPa 50 MPa 50 MPa
Prob. 2.9-10. At room temperature (70°F) and with no axial load (P = 0) the extensional strain of the prismatic bar (Fig. P2.9-10) in the axial direction is zero, that is, € = 0. Subsequently, the bar is heated to 120°F and a tensile load P is applied. The material properties for the bar are: E = 10 × 10³ ksi and a = 13 x 10-6/F, and the cross-sectional area of the bar is 1.8 in². For the latter load-temperature condi- tion, the extensional strain is found to be €x = 900 × 10 6. (a) Determine the value of the axial tensile load P. (b) De- termine the normal stress and the shear stress on the oblique plane NN'. (Note: The total strain is the sum of strain asso- ciated with normal stress o (Eq. 2.14) and the strain due to change of temperature AT (Eq. 2.8).) in. P Gage measures extensional strain Ex N N' 25° P2.9-10 X
A thin triangular plate ABC is fixed on side AB. The plate is strained such that all straight lines in the plate remain straight after deformation and that apex C is displaced to point C'as shown. Compute the following: a) the normal strains ex, ey and the shearing strain yxy at point C based on small deformation theory b) the normal strain at point A in the direction of AC based on small deformation theory c) the normal strains ex, ey and the shearing strain yxy at point C based on large deformation theory A 30° -200 mm. 3mm C" 1 I 1 1 60° 4mm
1. The stress condition on a two-dimensional infinitesimal material element is shown in Fig. 1 Fig. 1 60 MPа A 50 MPа В 30 MPа A. Describe the state of stress on: (i) Face A (ii) Face B B. State the sign convention for stress components on faces A and B in the: (i) Physical-space (ii) Mohr-Circle-space C. Draw the Mohr circle for the stress element in Fig. 1

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7-82. The material distorts into the dashed position shown. Determine the average normal strains along the diagonals AD and CF. 15 mm 30 mm 50 mm 200 mm 50 mm -150mm |F