 # 9b- Practice problem-longitudinal weld of a plate section

## Practice problem-longitudinal weld of a plate section.

This is a Practice problem for the longitudinal weld of a plate section., this is case 4 for the shear lag factor table D3.1-CM-14. and also can be considered as case 4a based on CM-15 and related specification -2016.

In this post, we will solve two solutions the first solution is based on CM-14 and the second solution is based on CM-15.
A given WT5x15 section Of A922 steel with transverse weld to its flange as shown in Figure P3-32 is required to find The LRFD and ASD values neglecting the block shear.

As we can see from the next picture, for table D3.1 shear lag factors for connections to tension members, for longitudinal weld it is case 4, here it is only for plates where the tension load is transmitted by longitudinal weld only. The shear lag factor depends on the width of the joint w and establishes a relation between the length of connection L and width W.

### Estimate the minimum value of shear lag factor U based on CM-14.

1-From the given Data for the ASTMA36, we can get the yield stress Fy=36 ksi and the ultimate stress Fult as equal to 58 ksi.

From the given section of PL3/8×5 , the width of plate w=5 inches, we cannot estimate the minimum shear lag factor for plates. by diving the area of the connected area of the whole area since it is not allowed by the code for plates.

2- The length of connection is given by the given section as equal to 5 inches.

3- From the given section of PL3/8×5, the width of plate w=5 inches .

4- There are three cases based on the relation between L and W for the value of shear lag factor U. For this practice problem, we have L=W, and the U value will be found to be equal to 0.75.

### The estimation of the effective area-CM-14.

The net area of the -longitudinal weld of a plate section is equal to the gross area of the plate which is (width by thickness)=5×3/8=1.875 inch2.

The effective area can be found by multiplying the U*net area and the value is equal to 1.406 inch2.

### The estimation of the Nominal strength for Practice problem-longitudinal weld of a plate section.

We have two cases for the nominal strength, the first case is the case of tensile yielding for which we consider the area as the full area and the tensile strength is equal to yield stress multiplied by the area and can be found as (1.875*36)=73.125 kips.

While the second case for tensile strength is the case of rupture strength in which the value is found to be equal to the effective area multiplied by the ultimate stress. and can be found as (1.46*58)=81.55 kips.

#### LRFD strength for Practice problem-longitudinal weld of a plate section.

Multiply the first value of the strength due to yield by the reduction value of PHi equal to 0 .90, we can get the LRFD strength due to yielding as equals 65.80 kips.

Multiply the second value of the strength due to rupture by the reduction value of PHi equal to 0 .75, we can get the LRFD strength due to rupture as equals 61.16 kips.

We will select the lesser value as our final LRFD strength which equals 144 kips, this is an indication that the LRFD strength is governed by rupture.

#### ASD strength for Practice problem-longitudinal weld of a plate section.

Multiply the first value of the strength due to yield by the reduction value (1/omega) equal to (1/1.67), we can get the ASD strength due to yielding as equals 43.79 kips.

Multiply the second value of the strength due to rupture by the reduction value of (1/omega) equal to (1/2), and we can get the ASD strength due to rupture as equals 40.775 kips.

We will select the lesser value as our final ASD strength which equals 41 kips, this is an indication that the ASD strength is governed by rupture.

### Estimate the shear lag factor U based on CM-15.

Referring to Table D3.1 for shear lag factor based on CM-15. The item number for shear lag factor U for the longitudinal weld to a plate is termed 4a and includes also other structural items that have also longitudinal weld unlink, the previous version of table D3.1 for Cm-14. The U value is estimated by the product of (3L^2/3l^2*w2) multiplied by (1-1- x̅/ L). the second term is set equal to 1 for plates.

1-From the given Data for the ASTMA36, we can get the yield stress Fy=36 ksi and the ultimate stress Fult as equal to 58 ksi.

From the given section of PL3/8×5, the width of plate w=5 inches,.

1- The length of connection is given by the given section as equal to 5 inches.

2- From the given section of PL3/8×5, the width of plate w=5 inches .

3- The shear lag factor U equals(3*5^2/(3*5^2+5^2)=0.75 which is the same value as estimated by CM-15.

### The estimation of the effective area-CM-15.

The net area of the -longitudinal weld of a plate section is equal to the gross area of the plate which is (width by thickness)=5×3/8=1.875 inch2.

The effective area can be found by multiplying the U*net area and the value is equal to 1.406 inch2.

### The estimation of the Nominal strength for Practice problem-longitudinal weld of a plate section.

We have two cases for the nominal strength, the first case is the case of tensile yielding for which we consider the area as the full area and the tensile strength is equal to yield stress multiplied by the area and can be found as (1.875*36)=73.125 kips.

While the second case for tensile strength is the case of rupture strength in which the value is found to be equal to the effective area multiplied by the ultimate stress. and can be found as (1.46*58)=81.55 kips.

#### LRFD strength for Practice problem-longitudinal weld of a plate section.

Multiply the first value of the strength due to yield by the reduction value of PHi equal to 0 .90, we can get the LRFD strength due to yielding as equals 65.80 kips.

Multiply the second value of the strength due to rupture by the reduction value of PHi equal to 0 .75, we can get the LRFD strength due to rupture as equals 61.16 kips.

We will select the lesser value as our final LRFD strength which equals 144 kips, this is an indication that the LRFD strength is governed by rupture.

#### ASD strength for Practice problem-longitudinal weld of a plate section.

From the estimated calculation the selected ASD value is 41 kips, the full data is shown in the next slide image.