tutorial- 8: combined loadings - chapter 1

2005 Pearson Education South Asia Pte Ltd

TUTORIAL-6 : Combined Loadings

1

Stress in Shaft due to Bending Load and Torsion

T

x y

z

A shaft has a diameter of 4 cm. The

cutting section shows in the figure is

subjected to a bending moment of 2 kNm

and a torque of 2.5 kNm.

Determine:

1. The critical point of the section

2. The stress state of the critical point.

PROBLEM-1

TUTORIAL- 8: Combined Loadings



2

T

x y

z

Analysis to identify the critical point

Maximum shear stresses occur at the

peripheral of the section or on the

outer surface of the shaft.

Due to the torque T

Due to the bending moment M

Maximum tensile stress occurs at the

bottom point (A) of the section.

Conclusion: the bottom point (A) is the critical point

A

PROBLEM-1




3

PROBLEM-1

T

x y

z

Stress components at point A

Due to the torque T

Due to the bending moment M

A

198.94 MPa 4

(0.02)

2)(2500)(0.0

2J

cTτ

318.31 MPa 4

4(0.02)

2)(2000)(0.0

zI

cM

318.31 MPa

198.94 MPa

Stress state at critical point A

x = 318.31 MPa txy = 198.94 MPa




4

Stress in Shafts Due to Axial Load, Bending and Torsion

A shaft has a diameter of 6 cm. The cutting section shows in the

figure is subjected to a compressive force of 2500 N, a bending

moment of 800 Nm and a torque of 1500 Nm.

Determine the stress state of point A.

PROBLEM-2




5

Analysis of the stress components at point A

Due to comprsv load:

Due to torsional load: J

cTA t

A

FA'

Due to bending load: z

'A'I

cM (compressive stress)

PROBLEM-2

MPa88.0)60(

25002

4

A'

MPa35)30(

30)(1500000)(4

2

t A

MPa72.37)30(

)30)(800000(4

4

'A'




6

Stress state at point A

Shear stress: txy = tA = 35 MPa

Normal stress: x = A’ + A”

txy

x

PROBLEM-2

= (– 0.88 – 37.72) MPa

= – 38.6 MPa




7

The screw of the C-clamp exerts a compressive force of

500 N on the wood blocks. Sketch the stress distribution

along section a–a of the clamp. The cross section there is

rectangular, 0.75 cm by 0.50 cm.

PROBLEM-3




8

PROBLEM-3




9

The joint is subjected to a force of 250 N as shown. Sketch

the normal-stress distribution acting over section a–a if the

member has a rectangular cross section of width 0.5 cm

and thickness 0.75 cm.

PROBLEM-4




10

PROBLEM-4




11

PROBLEM-4




12

The offset link supports the loading of P = 30 kN.

Determine its required width (w) if the allowable

normal stress is σ allow =73 MPa. The link has a

thickness of 40 mm.

PROBLEM-5




13

PROBLEM-5




14

PROBLEM-5




15

The symmetrically loaded spreader bar is used to lift the 20-kN

tank. Determine the state of stress at point A and B, and

indicate the results on a differential volume elements.

PROBLEM-6




16

PROBLEM-6




17

PROBLEM-6


A B



PROBLEM-7


tutorial- 8: combined loadings - chapter 1

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