13-The relation between Block shear and coped beams.

13-The relation between Block shear and coped beams.

The relation between Block shear and coped beams.

Brief content of the video.

A discussion of  2 items, the first item is a sample for the block shear various patterns for a given section acted upon by tension force.

Block shear and Coped beams and the different names used for copped beams.

Topics included in our discussion are shown in the next slides.

Block shear definition.

We continue discussing Block shear path graph, the second subject we will discuss is the coped beam and the UBS value condition.
From the site Beginner structural engineering .com / BGSCM14/BGSC. Prof. Thomas Bartlett (Bart) Quimby describes the block shear in the case of the W section, I beam, which is subject to block shear.

There are two modes of failure, the first mode of failure, for which, one part was separated, contains the part of the web, plate, and bolts are included.

Illustration for block shear.

The second mode of failure, contains a part of the flange and web, in a form of a T-section,  together with the plate and bolts.

Looking to block shear path no.1, the separated part, which is the middle part, comes out with the bolts.  This is the tension force developed due to the applied tension force.

The tension developed is perpendicular to the left face, while the shear force developed is in the parallel plane to the direction of the force, due to equilibrium, the force is applied to the right while the sum of the inner forces acts at the left.

Due to balance at the joint, the force acting to the left will produce shear forces acting to the right, also the tension force as well will act to the right.
This tension acts parallel to the external tension force and can be considered perpendicular to the section.
Let us have a look at the block shear path 2, the separated part in the form of T section, this is the tension force these are the faces parallel to the direction of the force.

But the shear force developed will be only for one face. since, there is no cut in the lower line of bolts, unlike the first path 1 which has two shear faces,  here there is shear and tension in the perpendicular face.
The last view is for the block shear path no.3.where the cut includes two lines, for the first line is made vertically up and will have developed tension force.
The second line, which passes through the bolts will have a shear force, the sketch to the right shows the equilibrium of the forces.
The side view is showing the T section.

The different paths for block shear.

This is the general equation used for estimating Rn value for block shear failure, for which Agv, is the gross area resisting the shear force component of the tensile force, Anv is the net area resisting shear force after deducting the area for bolts.

The AISC equation for the block shear strength.

UBS, a factor for the uniformity of stress,  is 1 or less than 1, based on the type of connection. as indicated in the commentary

What are the Coped beams?

 The coped beam is a cut in the secondary beam, which is carried by the main beam. As in the sketch shown.

For the two beams carried by the main beam, a cut is made for the two flanges on the right and left of the secondary beams, a connection is created by the use of angles bolted at the web of the main beam.

In the second sketch at the right, the beam is required to be installed, via the crane, between two columns. The cross-section is the section for the column and the lateral coped beam.

What are coped beams?

We can see a shear plate. the bottom flange coped to avoid interference with a shear plate, a cut is made to the bottom flange to facilitate the handling of the beam by crane.

Let us have a look at the next slide, In some cases, field conditions May dictate the requirement of a cope, for example, the previous figure 11-1, shows a beam framing into the web of the column.

When this beam is erected to its final position, it is dropped down in between the Column flanges.

This particular Beam would require a coped bottom flange, to be placed without an obstruction. that is why the bottom flange was cut.
Other common coped beam connections are shown in figure 11-2, for the first figure, there is a secondary beam resting on the main beam, the reaction developed due to loading.

The cut is made to support the secondary beam on the top of the flange of the main beam, so a part of both of the web and flange was cut, let us examine the forces the section needs reinforcement, to increase Sx, the bending section modulus of the beam.
After the cut of the section, it is reduced into a T section, as shown above, so the reinforcement needed is done by using two plates at each side of the web of the T section.

In the next section, in part b, the top flange cope, where the cut is made in the flange, and includes an angle to connect the secondary beam to the main beam, where the cut is only done for the top flange. In the next sketch part c, the cut is done for the upper and lower flange of the secondary beam, coped at both flanges. The section of the beam is large and due to the large reaction, plenty of bolts are to be used.

The code specifies different shapes with different names, as we are going to see. A beam cope is defined as the removal part of the beam web and flange, here a cut for both flange and web is made.

This is cope by name. While in the second section, a block name was given after cutting two parts of the flange. A block is the removal of the flange only, so the web was not cut. A cut is the removal of the side of the flange in each of these cases, it is common to refer to any of them as copes since the analysis and design procedures are similar.

This means, that regardless of the different names, all can be considered as coped beams.

The different types of coped beams.

 Cases where UBS=1

From the AISC commentary, these are the cases for the UBS value =1.
The new case is tension & shear due to the reaction that pushes. and thus creates shear stress in the group of bolts, which are in the vertical direction, and tension is developed due to the resistance of the tensile area and has a uniform stress distribution for The shear area close to the edge.

The second sketch is for the hanger connected to the gusset plate and here there is a diagonal member in a truss, the member is under tension force, so one face has shear stress and the other faces which have shear stress, and other faces which have Tension stress.
The other section is for the same connection, inclined member to a gusset plate, but welded.

The last case is the coped beam which is welded, this sketch is for single-Row beam end conditions, and this sketch is for angle ends, under tension .here we have a gusset plate.
For all these cases the UBS =1.

Aisc Commentary about copped beams.

 Cases where UBS=0.50

For the cases where the UBS=0.50, for the coped beam.
case b, Multiple-Row beam-end conditions, where the block shear occurs for two lines of bolts and tension area will have a triangular distribution of stresses, and these stresses are not uniformly distributed, and for the middle part b, web tear out in coped beam, because we have only one line of bolts, there is a uniform tension distribution of stresses.

While in the case of #c, we have shear area and tension area have a non-uniform stress distribution, these cases for UBS =0.50.

The case where Ubs the block shear coefficient=0.50.

This is the pdf file used in the illustration of this post.

The next posts are- post 19- Solution for Block Shear-Coped Beam Problem.

The next posts are- post 20- Aisc Tables 9-3a,b, and C for Block shear-coped beam.

The next posts are- post 21- Case 2 for block Shear-Coped Beam Problem.

There is a very useful external link-Block Shear Rupture. Chapter 3-tension members-A Beginner’s Guide to the Steel Construction Manual, 14th ed.

The related coped beam posts are:

Solutions for Block Shear-Coped Beam Problem.
Aisc tables 9-3a,b, and C for Block shear-coped beam.

This is the next post Solved problem 5-7 for block shear

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