Bucking of Stress and Load : 642868

Question:

BUCKLING OF COLUMN: The wood column is fixed at its base and can be assumed fixed connected at its top. Determine the maximum eccentric load P that can be applied without causing the column to buckle or yield. Take E =

12GPa and 𝜎𝑦= 15 MPa

Tutorial Worksheet 03

COMBINED LOADINGS: Determine the state of stress at point A on the cross section of the pipe assembly at section a–a.

Tutorial Worksheet 03

BENDING STRESS: If the beam is subjected to a bending moment of M = 30 kN.m, determine the maximum bending stress in the beam.

Tutorial Worksheet 03

TRANSVERSE SHEAR: Determine the maximum shear stress in the T-beam at point C. Show the result on a volume element at this point.

Tutorial Worksheet 03

TORSION: The 30-mm-diameter A-36 steel shaft is subjected to the torques shown.

Determine the angle of twist of the end B

Answer:

1)

COMBINED LOADINGS: Determine the state of stress at point A on the cross section of the pipe assembly at section a–a.

1

Solution

Axial load P= 1000 N

Shear load V = 1500 N

Diameter d = 40 mm

Area of shaft

A = 1256.64 mm^2

Axial stress

From above values

 = 795.8 KN/M^2

As A lies in neutral axis ,so

2

Now Moment  M = 1500 * 400 /1000

M = 600 Nm

Now Bending Stress

Y=d/2

Now Shear Stress

C   =   T r / J

T = 1000 * 400/1000

T = 400Nm

Put all values in torsion equation

Question 2 BENDING STRESS:If the beam is subjected to a bending moment of M = 30 kN.m, determine the maximum bending stress in the beam.

4

Solution

As Given M = 30 KNm

Neutral Axis of a section Y = 200 /2

Y= 100mm

Moment of inertia = 26840000 mm^4

Tutorial Worksheet 03

TORSION: The 30-mm-diameter A-36 steel shaft is subjected to the torques shown.

Determine the angle of twist of the end B

Solution

A-36 shear modulus G =75 GPA

D =30 mm

For series          

J =79521.56 mm^4

Taking clockwise as positive

BUCKLING OF COLUMN: The wood column is fixed at its base and can be assumed fixed connected at its top. Determine the maximum eccentric load P that can be applied without causing the column to buckle or yield. Take E =

12GPa and 𝜎𝑦= 15 MPa

5

Solution

As this is the case of strut having both ends fixed

As According to bucking load formula

For both ends fixed  n=4

E =12 GPA

L = 3048 mm

I = 533333.3 mm^4

Put all values in formula we get ,

Pcr =27.196 KN

Calculate Maximum eccentric load P

Calculating from above formula we get

P = 18.17 Kn

TRANSVERSE SHEAR: Determine the maximum shear stress in the T-beam at point C. Show the result on a volume element at this point.

As shear stress

V = maximum shear force

Q = Ay

I = moment of inertia

t= thickness

Q =216000 mm^3

I = 8775000 mm^4

t =30 mm

 

Ra                                                                                                       Rb

Calculate reaction

Rb = 5KN

Ra = 40KN

Now put all values in Shear stress formula