Tutorial on Combined Bending & Axial Force PDF

Preview

Summary

Combined Bending & Axial Force...

Description

Mechanics of Structures 2A Example Sheet 3 - Combined bending & axial force 1. The cantilever beam shown in Fig.1 has a rectangular cross-section 100 mm deep by 50 mm wide. It carries a vertical load of 1 kN and an axial load of 200 kN at the free end as shown. (a) Determine the position of the neutral axis at the support. (b) Calculate the maximum tensile stress.

1 kN

200 kN 1m Fig. 1 2. A short box member carries an eccentric load as shown in Fig.2. The box is 80 mm × 80 mm with a constant wall thickness of 10 mm. (a) Calculate the maximum and minimum stresses on the cross-section X-X (b) Calculate the position of the neutral axis under the combined stresses. (c) Draw the stress distribution, indicating clearly the key values. 3. A stub column consists of the unsymmetrical I-section shown in Fig.3. Calculate the minimum distance from the bottom edge that a 500 kN compressive load can act on the web so that the compressive stress nowhere exceeds 160 N/mm2.

X

300mm

X

12mm

G 500 kN

300mm

y 80 mm

8mm

60mm

12mm

72 kN 100mm

80mm

2

y = 199.3mm, A = 7008 mm 6 4 I = 96.6×10 mm

10mm

Fig. 2

Fig. 3

-1-

4. A steel cantilever beam AB is made from the T-section shown in Fig.4. The overall depth of the section varies linearly from 200 mm at A to 100 mm at B. The beam is pulled by a uniformly distributed tensile load of 70 N/mm2 acting over the whole cross-sectional area at B. The allowable tensile stress is 115 N/mm2. (a) Calculate the safe uniformly distributed vertical load q that the beam can carry. (b) For this loading, calculate the maximum compressive stress in the beam.

q per unit length

A

B 100 mm

200 mm 2500 mm

150mm 10mm 200mm at A 100mm at B 6mm

Fig. 4

Solutions 1. (a) neutral axis 117 mm below soffit (b) 52 N/mm2 2. (a) 149 N/mm2 tension, 98 N/mm2 compression (b) neutral axis 108 mm from line of action of applied force. 3. 113.4 mm 4. (a) q = 2.64 kN/m (b) max. compressive stress = 137.7 N/mm2

-2-

2

70 N/mm...