$σ_{x}, σ_{y} a n d τ_{x y}$ and normal and shear stresses on the x and y faces. What is the radius of Mohr's circle in terms of these stresses?

$\frac{σ_{x} - σ_{y}}{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{σ_{x} - σ_{y}}{2} + τ_{x y}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + τ_{x y}^{2}}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{{(\frac{σ_{x} + σ_{y}}{2})}^{2} - τ_{x y}^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$\sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + τ_{x y}^{2}}$

Radius of Mohr's circle
$= \sqrt{{(\frac{σ_{x} + σ_{y}}{2})}^{2} + {(- τ_{x y})}^{2}}$

$= \sqrt{{(\frac{σ_{x} + σ_{y}}{2})}^{2} + {τ_{x y}}^{2}}$

Suggest Corrections

Similar questions

Q. On the element shown in the given figure, the stresses are:

σ_{x} = 110 M P a

$σ_{y} = 30 M P a$

$τ_{x y} = τ_{y x} = 30 M P a$

$σ_{1}, σ_{2}$

The radius of Mohr's circle and the principal stresses $τ_{1}, τ_{2}$ are (in MPa)

The equation of Mohr's circle is given by $(σ - 4)^{2} + τ^{2} = 9$ where $σ$ is the normal stress and $τ$ is the shear stress. The maximum shear stress is units. ,

Q. The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the x and y directions are 100 MPa and 20 MPa respectively. The radius of Mohr's stress circle representing this state of stress is

Q. Consider the following statements?
1. The maximum shear stress is one half of the normal stress in the case of uniaxial stress field.
2. In biaxial stress field, acted upon by normal stresses unaccompanied by shear stresses, the maximum shear stress is any one of the normal stresses.
3. The Mohr's stress circle will be tangential to the vertical axis in the case of uniaxial stress field.
Which of the above statements are correct?

Q. At a point in a piece of stressed material the stresses are :

σ_{x} = α K N / m^{2}

$τ_{x y} = τ_{y x} = β K N / m^{2}$

Although the values of $α$ and $β$ are not known yet the principal stresses are equal to each other being $(5 k N / m^{2}) .$ What is the radius of Mohr's circle?

Join BYJU'S Learning Program

σx,σyandτxy and normal and shear stresses on the x and y faces. What is the radius of Mohr's circle in terms of these stresses?

The correct option is C √(σx−σy2)2+τ2xy Radius of Mohr's circle =√(σx+σy2)2+(−τxy)2 =√(σx+σy2)2+τxy2

$σ_{x}, σ_{y} a n d τ_{x y}$ and normal and shear stresses on the x and y faces. What is the radius of Mohr's circle in terms of these stresses?

The correct option is C
$\sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + τ_{x y}^{2}}$

Radius of Mohr's circle
$= \sqrt{{(\frac{σ_{x} + σ_{y}}{2})}^{2} + {(- τ_{x y})}^{2}}$

$= \sqrt{{(\frac{σ_{x} + σ_{y}}{2})}^{2} + {τ_{x y}}^{2}}$