A tie bar is made of a material having a tensile strength of 231MPa and has to carry a load of 225kN. What is the diameter of the bar if a factor of safety of 7 is applied?

Where do I begin?

Required capacity of bar (in tension)

=225kN*7
=1.575 MN
Tensile strength = 231 MPa
Area required
=1.575 MN / 231 MPa
=0.006818 m²
=6818 mm²

From πr²=6818
radius=√(6818/π)
= 46.6 mm (or more)

To begin solving this problem, let's first determine the maximum allowable load for the tie bar considering the factor of safety.

Step 1: Calculate the maximum allowable load:
Maximum allowable load = Load / Factor of safety

Given that the load is 225 kN and the factor of safety is 7,
Maximum allowable load = 225 kN / 7
Maximum allowable load = 32.14 kN

Next, we need to determine the cross-sectional area required to withstand this load.

Step 2: Calculate the cross-sectional area:
Cross-sectional area = Maximum allowable load / Tensile strength

Given that the tensile strength is 231 MPa (Millipascals) and the maximum allowable load is in kilonewtons (kN), we need to convert the tensile strength to kN.

1 MPa = 1 N/mm² (Newton per square millimeter)
1 kN = 1000 N (kilonewton)

So, converting 231 MPa to kN:
231 MPa = 231 N/mm² = 231 N/mm² * (1 kN / 1000 N)
231 MPa = 0.231 kN/mm²

Now, we can calculate the cross-sectional area:
Cross-sectional area = 32.14 kN / 0.231 kN/mm²
Cross-sectional area = 139.4 mm²

Lastly, we can determine the diameter of the tie bar using the cross-sectional area.

Step 3: Calculate the diameter:
The cross-sectional area of a circle can be calculated using the formula:
Cross-sectional area = π * (diameter/2)²

Rearranging the formula to solve for the diameter:
(diameter/2)² = Cross-sectional area / π
diameter/2 = √(Cross-sectional area / π)
diameter = 2 * √(Cross-sectional area / π)

Substituting the cross-sectional area value into the formula:
diameter = 2 * √(139.4 mm² / π)
diameter = 2 * √(44.33 mm²)
diameter = 2 * 6.65 mm
diameter ≈ 13.3 mm

Therefore, the diameter of the tie bar should be approximately 13.3 mm to withstand the given load with a factor of safety of 7.

To find the diameter of the tie bar, you can use the formula for stress, which is defined as force divided by area:

Stress = Force / Area

First, let's calculate the force by converting the load from kilonewtons (kN) to newtons (N):

Load = 225 kN × 1000 N/kN
Load = 225,000 N

Now, let's calculate the area of the bar using the tensile strength and the factor of safety:

Tensile Strength = Stress × Safety Factor
Area = Load / (Tensile Strength × Safety Factor)

In this case, the safety factor is 7. Rearranging the formula, we get:

Area = Load / (Tensile Strength × Safety Factor)

Finally, to find the diameter of the bar, we can use the formula for the area of a circle:

Area = π × (Diameter/2)^2

Rearranging the formula, we get:

Diameter = √(4 × Area / π)

Now that we know how to approach the problem, we can start calculating the diameter of the bar.