Additional lecturebook examples 65 ME 323

Example 18.3 A tubular steel column, with the cross section shown below and a length of L, is subjected to an axial load of P . The material of the column has a Young’s modulus of E and a yield strength of σY . If the column has fixed-free end conditions, what is the factor of safety for buckling?

b

2b

t

y

z

Additional lecturebook examples 66 ME 323

Example 18.5 The column shown below is clamped onto to ground at its bottom, with the top of the beam able to slide within a slot. The column carries an axial load of P. What is the largest load P that the column can withstand without buckling? Use h = 3t and L = 10h .

P

hL

x

z

y

t

Additional lecturebook examples 67 ME 323

Example 18.7 The truss shown is made up of members (1) and (2), each made up of a material having a Young’s modulus of E = 30×106 psi and have a solid circular cross section. The

diameters of members (1) and (2) are 0.5 in and1.0 in, respectively. Determine the largest load P that can be applied at joint C without buckling occurring in the structure. Consider only in-plane Euler buckling in your analysis.

P

B

C

D

48 in

36 in

21 in

28 in

2( )

1( )

Additional lecturebook examples 68 ME 323

Example 18.8 The truss shown is constructed from members (1), (2) and (3), with each member made up of a material having a Young’s modulus of E = 10×106 psi , a yield strength of

σY = 60×103 psi and each member having a solid circular cross section with a diameter

of d = 1 in . A force P = 10 kips is applied to joint C in the truss. Determine the maximum

length L allowed to prevent buckling in the truss. State whether the Euler theory or the Johnson theory was used in arriving at your result. Provide a justification for the choice of buckling theory used here.

BC

D

L

P

1( )

3( )

2( )

3

4

Additional lecturebook examples 69 ME 323

Example 19.3 Shown below is a cantilevered W14 ×120 wide flange beam made up of steel, with

E = 29 ×103ksi . As shown in the Appendix of the textbook, this beam has a cross-

sectional area of A = 35.3in2 and a second area moment of I = 1380 in4 . Determine the slope and deflection at end C of the beam due to the loading shown.

4 kips / ft

A C 5 ft

x

y,v

5 ft

2 kips

B

Additional lecturebook examples 70 ME 323

Example 19.6 Determine the deflection curve v(x) for the beam shown below.

M0

A B C

x

y,v

a a

p0

p0

A B

x

y,v

a a

C P

V(x)

M(x)

x

x

θ(x)

v(x)

Additional lecturebook examples 71 ME 323

Example 19.7 Determine the deflection curve v(x) for the beam shown below.

M0

A B C

x

y,v

a a

p0

p0

A B

x

y,v

a a

C P

V(x)

M(x)

x

x

θ(x)

v(x)

Additional lecturebook examples 72 ME 323

Example 19.8 Determine the deflection curve v(x) for the beam shown below.

p0

A B

x

y,v

a a C

M0

A B C

x

y,v

a a

p0 P

a

V(x)

M(x)

x

x

θ(x)

v(x)