   # The bolt group shown in Figure P8.2-2 consists of 3 4 -inch-diameter, Group A slip-critical bolts in single shear. Assume that the bearing strength is adequate and use an elastic analysis to determine: a . The maximum factored load that can be applied if LRFD is used. b . The maximum total service load that can he applied if ASD is used. ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740

#### Solutions

Chapter
Section ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740
Chapter 8, Problem 8.2.2P
Textbook Problem
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## The bolt group shown in Figure P8.2-2 consists of 3 4 -inch-diameter, Group A slip-critical bolts in single shear. Assume that the bearing strength is adequate and use an elastic analysis to determine:a. The maximum factored load that can be applied if LRFD is used.b. The maximum total service load that can he applied if ASD is used. To determine

(a)

The maximum factored load that can be applied by using LRFD method.

### Explanation of Solution

Write the expression to calculate the load applied in the x-direction acting at an angle of 30°.

Px=Pcosθ ….. (I)

Here, the total load is P and load component in x direction is Px.

Substitute 30° for cosθ in Equation (I).

Px=Pcos30°=0.866Pk

Write the expression to calculate the load applied in y-direction at acting at angle of 30°.

Py=Psinθ ….. (II)

Here, the total load is P and load component in y direction is Py.

Substitute 30° for sinθ in Equation (II).

Px=Psin30°=0.5Pk

Write the expression for the load which is coming on each of the bolt in x-direction.

Pex=Pxn     ...... (III)

Here, the number of bolts is n and Pex is the load coming on each bolt in x direction.

Substitute 0.866Pk for Px and 10 for n in Equation (III).

Pex=0.866Pk10=0.0866Pk

Write the expression for the load which is coming on each of the bolt in y-direction.

Pey=pyn     ...... (IV)

Substitute 0.5Pk for Py and 10 for n in Equation (IV).

Pey=0.5Pk10=0.05Pk

Calculate the eccentricity of the load that is the distance from the middle of the connection to the point of load in both x and y directions from the diagram given below. The following Figure-1 represents the bolt connection.

Figure-(1)

Calculate the distance of the load from middle of connection.

ex=3in+3in+4in=10in

ey=5.5in2=2.75in

Here, the eccentricity in x direction is ex and, the eccentricity in y direction is ey.

Write the expression for the moment for x-axis about midpoint of the connection between the bolts.

Mx=Py×ex ..... (V)

Here, the moment generated is x direction is Mx.

Substitute 0.5Pk for Py and 10in for ex in Equation (V).

Mx=0.5Pk×10in=5Pin-k

Write the expression for the moment for y-axis about midpoint of the connection between the bolts.

My=Px×ey ..... (VI)

Here, moment generated is y direction is My.

Substitute 0.866Pk for Px and 2.75in for ey in Equation (VI).

My=0.866Pk×2.75in=2.382Pin-k

Write the expression for the moment for y-axis and x-axis about the midpoint of the connection between the bolts.

M=(Mx+My) ..... (VII)

Here, the total moment generated is M.

Substitute 5Pin-k for Mx and 2.382Pin-k for My in Equation (VII).

M=(5Pin-k+2.382Pin-k)=7.382Pin-k

Write the expression to calculate the location of the centroid with respect to top right of the critical bolt.

x¯=(n×d)T ..... (VIII)

Here, the number of bolts is n, the distance of the bolts is d and the total number of bolts is T.

Substitute the values in Equation (VIII).

x¯=(2×3in)+(2×6in)+(2×9in)+(2×12in)10=6in

Write the expression to calculate the location of the centroid with respect to top right of the critical bolt.

y¯=(n×d)T ..... (IX)

Substitute the values in Equation (IX).

y¯=5×5.5in10=2.75in

Write the expression to calculate horizontal and vertical components of the loads caused due to eccentricity.

(x2+y2)=(6in)2×4+(3in)2×4+(2.75in)2×5+(5.5in2.75in)2×5=255.6in2

Write the expression for the load coming on that bolt due to eccentricity.

Pmx=M×y(x2+y2)

To determine

(b)

The maximum total service load that can be applied by using ASD method.

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