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

Assignment Help:

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.


Related Discussions:- Examine the state of stress at the junction of flange

Breakwaters - harbour layout, Breakwaters: A breakwater is an artific...

Breakwaters: A breakwater is an artificial structure constructed in the sea to protect ships from the effect of waves and storms. Three types of breakwaters are common :

Calculate carbon intensity, how to calculate the carbon intensity (gC/MJ) f...

how to calculate the carbon intensity (gC/MJ) for gasoline ( C7H16 ) , we have the Energy Density = 32.2 MJ/L Fluid Density = 0.727 g/mL

How the raft is designed as a floating foundation, A raft, 9 m × 27 m, is f...

A raft, 9 m × 27 m, is founded at a depth of 3 m in sand with a value of  N = 25 up to great depth. Verify the total load which the raft can support. If the raft is designed as

Calculate the effective annual interest rate, A credit card advertises a no...

A credit card advertises a nominal rate of 18% compounded monthly. If no monthly payments are made, the effective annual interest rate is most nearly: The actual rate is, (18%

Yugty, #quesjjhjhhjtion..

#quesjjhjhhjtion..

Survey, how can I use reciprocal type of leveng method to level a ground, a...

how can I use reciprocal type of leveng method to level a ground, and a procedure

Differentiate between concrete and tendons, Differentiate between concrete ...

Differentiate between concrete and tendons In the case of pre-tensioned concrete members, the transfer of prestress takes place due to the bond between concrete and tendons. In

Define the meaning of grout - concrete, Define the meaning of Grout - Concr...

Define the meaning of Grout - Concrete Grout should be made with any type of recommended cement and using water of a required quality. If very large size ducts are to be groute

Solid mensuration, If the diameter of the base remains constant, by what fa...

If the diameter of the base remains constant, by what factor should the altitude be multiplied to produce a cone with twice volume as the original

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd