### Design Procedure Review – 02, Transverse Fillet Weld by Kotur Raghavan

**General**

It would be hard to come across
structures and mechanical assemblies which do not contain welded connections.
However, in almost all the stress analysis tasks using FEA the weld geometries
are not explicitly accounted for. Components which are welded together are
assumed to be rigidly connected. One of reasons is the challenges involved
because of geometric complexities. Moreover, welded connections are normally
configured based on industry standards.

All the same, we find chapters on
design of welds in all books of structural and mechanical design. One such
problem is taken up for study in the present article. This is the second in the
DPR series of articles.

**Transverse Fillet Weld**

The configuration taken up for
study is shown in Fig. 1 below. Load transfer takes place between the plate 1
and plates 2 through the welds 3.

Fig. 1

The present study is in the
context of the design procedure described by Shigley and Minschke in their book
*Mechanical Engineering Design, Sixth
edition, Page 529*.

Fig. 2

The authors of the book have used
the free body diagram shown in Fig. 2 above. The components of the force are
the normal force **N** and the shear
force **S** acting on the throat section
as shown. These forces on the throat section are assumed to be generating
uniform stress fields. Through solution of equilibrium equations, they have derived
an important design relation for the maximum von Mises stress Se as

Where L is the length
of the plates and weld.

**Analysis**

Finite element model
study is taken up for assessment of the aforementioned design information. 2D
plane stress model is analysed. Because of symmetry only one half of the
assembly is considered for analysis. The details of the model are shown in Fig.
3 below.

Fig.
3

The allowable stress of
the weld material is assumed to be 200 MPa. For this allowable value and a
thickness of 20 mm the load limit for the weld works out 1852 newtons per unit
length. This load is applied in the form of uniform pressure (92.6 MPa).

Fig.
4

The overall results are
presented in Fig. 4 above. The high stress is at the corner of the weld and is
due to singularity. As the region of interest is the weldment, we will focus on
the prevailing stresses there.

Fig.5

The weld area and the
equivalent stress contours in the region are given in Fig. 5 above. The range
is from zero to the allowable stress (200). The grey coloured regions have
stresses higher than the allowable. The
high stress regions also include spurious stresses due to singularity. As the
throat area is critical, it is necessary to assess the nominal value of stress
at the corner A. One way of addressing this task is to compute linearized
stresses across the section AB.

Fig.
6

In Fig. 6 above,
linearized von Mises stresses across the section AB are shown. The graph has
two important results. The section under consideration has a membrane component
of 173 MPa and a Membrane + bending component of 309 MPa. The value of 309 is
the nominal stress at the corner A. This value is still high in comparison with
the allowable value of 200. At this
point we will take a look into ASME’s Design by Analysis (DBA) guidelines.

**DBA Guidelines**

DBA guidelines are part
of the ASME’s Boiler and Pressure Vessel Codes, Section VIII, Division 2. As
per this, stresses across any section can be categorized into membrane (uniform
component), bending (linearly varying component) and the Peak (additional due
to stress raisers). From a strength point of view, as per the code, the
allowable stress, which is normally the yield stress divided by the factor of
safety, applies to the membrane component. The allowable limit for membrane +
bending component is 1.5 times that for the membrane component.

The present author has earlier
stated that the machine design books and the mode of teaching make no reference
whatsoever to the stress categories. See

https://www.fembestpractices.com/2020/11/traditional-design-teaching-chief.html.

This shortcoming
results in conservative designs.

In the present case
study, the allowable membrane stress is 200 and therefore the allowable (M + B)
component of stress is 300 MPa. The computed membrane stress is 173 which is
well within the allowable limit. The (M + B) component is 309 and is thus
marginally unsafe (by 3 per cent). If the higher allowable is not considered
the design would have been unsafe by a big factor.

**Stresses along the throat**

As stated already, the
normal as well as the shear stress at the throat section are assumed to be
uniform in the design using hand calculations.

Fig.
7

In Fig. 7 above, the
computed values of normal and shear stresses are plotted along AB. The two
corresponding curves are named Normal-FE and Shear-FE in the graph. The two other
lines, in broken lines, show the values of these as assumed in the Machine
Design (MD) text book. The shear stress distributions are in reasonable
agreement. Also the assumed value is higher than the computed value for most
part. The assumed value of normal stress is lower than the computed value for
more than 50 per cent of the path. This is the main reason for the design
assumption turning out to be non-conservative.

**Summary**

·
The design procedure, as presented in the
referred text book, has been thoroughly reviewed.

·
The assumption of uniform stress
distribution along the throat section has turned out to be non-conservative.
The nominal value of (M+B) component is observed to be more than one and half
times the allowable value (309 as against 200)

·
However, if the DBA guidelines are
considered, the design will be only marginally unsafe (309 as against 300).

·
Whether the DBA guidelines are taken into
consideration or not, the fact is that the weld is acceptable up to about 97
per cent of the applied load. Thus the conservatism involved in treating the
(M+B) component on par with the membrane component has almost fully compensated
for the non-conservative assumption of uniform stress distribution. This is
sort of ironical situation.

·
An important takeaway of this study is
the use of stress linearization and its application for certifying the design
adequacy. In general, linearization is possible only through finite element
simulation.

ASME’s DBA guidelines, as far as bending component is concerned, has sound theoretical basis and is related to the concept of plastic moment of a section. This is very important design concept. It is the author’s considered opinion that the undergraduate students in mechanical and structural engineering need to be exposed to this.

(In the introduction). One more reason why welds are not explicitly modelled is that elastic properties in the welded zones are very difficult to establish/predict

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