Answered: The stresses acting on element A in 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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Question

The stresses acting on element A in the web of a train rail are found to be ‘75 (MPa)’
tension in the horizontal x-direction and ‘90 (MPa)’ compression in the vertical
y-direction. Also, shear stresses of magnitude ‘40(MPa)’ act in the directions shown in
the figure.
a) Draw Mohr’s circle for the state of stress.
b) Determine the stresses (σx', σy' and τxy') acting on an element oriented at an angle
‘D=-10 ˚’ from the horizontal. Show these stresses on a sketch of an element
oriented at this angle

Note: If the angle D is positive, then the shear stress is in the direction shown on
the unit element figure; if it is a minus sign, then the shear stress is in the
opposite direction shown on the unit element figure.

Appendix B
Useful Formulas
Bending
P- M2y – Myz
Iz
1
M
bh3
I
I ==r
4
Ox = 7-
-=
EI
12
A
ly
Principal stresses
My
VQ
3V
Tave =
It
Ттах —
2 A
Or = -
Transformations of plane stress
Ox + Oy + (OxOy) cos(20) + Txysin(26)
2
2
Txy
(0x – Oy
(*,)
sin(20) + Txycos(20)
2
= -
Ox + oy = 0x + Oy
Ox + Oy
Oy
+ T,
(0x
(Ox
Отах,min
Tmax =
2
2
! (UM? + M? + T2
тах
Tall
Spherical Pressure vessels
pr
pr
Ттах
4t
Ospherical
2t
Deflection of beams
d²y_M(x)
dx2
EI
M IN
2.

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