Examine the state of stress at the junction of flange, Civil Engineering

Examine the state of stress at the junction of flange:

A beam of I-section as shown in Figure (a) is subjected to a bending moment of 84.928 kN m and a shear force of 106.1 kN. Examine the state of stress at the junction of flange and web.

1587_Examine the state of stress at the junction of flange.png

Figure

Solution

(In this case also the solution will be provided by stating the expressions for stress components, without their derivation which will be dealt with in addition.)

A neutral axis of the section will be the horizontal axis through the centroid of the section.

The bending stress at a layer 'y' above the neutral axis is given as,

σx = -My/I                                                                    . . . (iv)

here, I is the moment of inertia of the section and M is the bending moment on the section.

The shear stress at some layer is given as

 τxy= Q . Ay¯/Ib                                                              . . . (v)

here, Ay¯  is the moment of the area of that portion of the section above or below the layer about the neutral axis, b is the breadth of the layer and Q, the shear force at the section.

For the cross-section given, the moment of inertia is given as 2.1232 × 108 mm4. Total depth of beam = 400 mm.

∴ Neutral axis is at a depth of 200 mm from top.

A distance of the layer at junction of web and flange from the neutral axis is 180 mm.

Determination of Bending Stress

σx   = - My/I - 84.928 × 106 × 180/2.1232 × 108 = -72 N/mm2

Determination of Shear Stress

In this case Ay¯ will be given by the moment of the flange area about the neutral axis.

Ay¯ = 120 × 20 × (180 + 20/2)= 4.56 × 105  mm3

τxy = 106.1× 103 ×4.56 ×105/2.1232× 108×10 = 22.8 N/mm2

1624_Examine the state of stress at the junction of flange1.png

Thus, we get,

σ1  = 6.613 N/mm2

σ2  = - 78.613 N/mm2

τmax  = 42.613 N/mm2

You may obverse here in which the junction among flange and web will become the critical zone, while the shear force at the section is considerable. Therefore, experience will tell you, while to look for critical zones in various cases.

Posted Date: 1/30/2013 6:29:54 AM | Location : United States







Related Discussions:- Examine the state of stress at the junction of flange, Assignment Help, Ask Question on Examine the state of stress at the junction of flange, Get Answer, Expert's Help, Examine the state of stress at the junction of flange Discussions

Write discussion on Examine the state of stress at the junction of flange
Your posts are moderated
Related Questions
Q. Show the result of vulcanization? As a result of vulcanization, rubber molecules are cross-linked with sulphur. This cross-linking makes the rubber stronger. It allows the r


Q. Coatings at the back faces of abutments? There are many views on the necessity of application of protective coatings (can be in the form of two coats of paint) to the back f

A cylindrical concrete tank, 30 m external diameter, is to be prestressed circumferentially by means of  high-strength steel wire (E, = 2 x  10 5   N/mm 2 )  jacked  at 4 points, 9

Analyse the state of stress at the critical section: A prismatic bar of circular section with 80 mm diameter is subjected to bending moment of 5 kN-m and a torque of 7 kN-m. A

Define in biref about the Final Prestress The stress which exists after all losses of prestress have occurred substantially is known as final prestress. This may be calculated

pls explain about this field


Q. What do you mean by Plain elastomeric pads? Plain pads are used for light or moderate loadings. Plain pads have a tendency to bulge under heavy loadings. In order to reduce

Immersed tube method for underwater crossing includes the following basic construction steps: (i)  Prefabricating long tunnel units (concrete orsteel shell) in a dry-dock or shi