Shear Stress in beams

Question 1

If the bending moment at section 2 is greater than that at section 1 how are the difference of forces balanced

Answer 1

by a shear force, dF acting on the lower edge of the element

= QdM/I

*the first moment of the cross-sectional area (Q)
*second moment of inertia (I)
*M2 - M1 (dM)

Question 2

the first moment of the cross-sectional area (Q)

Answer 2

= A’ ȳ

*area of the cross-section (A’)
*height of the centroid of the partial area above the neutral axis of the cross-section (ȳ)

Question 3

distribution of longitudinal shear stress in a rectangular beam

Answer 3

τ = VQ / Ib

*second moment of inertia (I)
*base width of cross-section (b)
*first moment of the cross-sectional area (Q)
*vertical shear force (V)

Question 4

vertical shear force (V)

Answer 4

= dM / dx

*length of beam (dx)
*bending moments M2 - M1 (dM)

Question 5

maximum shear
stress (τmax) in the y direction

Answer 5

occurs on the neutral axis (y = 0)

= V h^2 / 8 I

*vertical shear force (V)
*height of cross-section (h)
*second moment of inertia (I)

Question 6

what is the shear force at the face of a cross-section

Answer 6

F = σA

*cross-sectional area (A)
*bending stress (σ)

Question 7

what is the change in longitudinal shear stress when we move in the z-direction

Answer 7

τ = Vhz / 2I

*second moment of inertia (I)
*height of cross-section (h)
*distance (z)
*vertical shear force (V)

Question 8

if you move in the z direction in a thin-walled structure how does the shear stress tend to change

Answer 8

linearly in accordance with the distance move

Question 9

if you move in the y direction in a thin-walled structure how does the shear stress tend to change

Answer 9

when the change in stress is plotted it forms a parabola with respect to distance along the structure

Question 10

maximum shear
stress (τmax) in the z-direction in a c beam

Answer 10

occurs on the neutral axis (z = b)

= Vhb / 2 I

*vertical shear force (V)
*height of cross-section (h)
*second moment of inertia (I)
*base length (b)

Question 11

maximum shear
stress (τmax) in the z-direction in an i-beam

Answer 11

occurs on the neutral axis (z = b/2)

= Vhb / 4 I

*vertical shear force (V)
*height of cross-section (h)
*second moment of inertia (I)
*base length (b)

Question 12

what occurs when you load an asymmetric beam

Answer 12

twisiting

Question 13

how do you avoid twisting in an asymmetric beam when a load is applied

Answer 13

move the load to an e distance away, shear centre

Question 14

how do you work out the shear centre (e)

Answer 14

= h^2 b^2 t / 4I

*height of cross-section (h)
*second moment of inertia (I)
*base length (b)
*thickness (t)