Design for flexure a simple beam 14 ft in length and having a total uniformly distributed dead load of 13.2 kips and a total uniformly distributed live load of 26.4 kips.
To design a simple beam for flexure, we need to determine the maximum moment and then select an appropriate beam size and material.
Step 1: Determine the total factored load:
The total factored load is the combination of the dead load and live load with appropriate load factors. Typically, the load factors for dead load and live load are provided by the design codes or standards. Let's assume the load factors for dead load and live load are 1.2 and 1.6, respectively.
Total factored dead load = dead load x load factor for dead load = 13.2 kips x 1.2 = 15.84 kips
Total factored live load = live load x load factor for live load = 26.4 kips x 1.6 = 42.24 kips
Step 2: Determine the maximum moment:
The maximum moment occurs at the mid-span of the beam under a uniformly distributed load.
For a simply supported beam with a uniformly distributed load, the maximum moment is given by:
Mmax = (wL^2) / 8
Where:
Mmax = maximum moment
w = uniformly distributed load per unit length
L = length of the beam
Let's calculate it:
w = (Total factored dead load + Total factored live load) / length of the beam
= (15.84 kips + 42.24 kips) / 14 ft
= 58.08 kips / 14 ft
= 4.15 kips/ft
Mmax = (4.15 kips/ft) x (14 ft)^2 / 8
= 3.60 kip-ft
Step 3: Select an appropriate beam size and material:
To select an appropriate beam size, you should consult a structural design code or a structural engineer. The beam needs to be strong enough to resist the maximum moment without excessive deflection.
Assuming we select a steel beam with a yield strength of 50 ksi, an appropriate beam size would be selected based on the calculated moment and the allowable stress for the material.
For example, the beam could be a W12x45 section, which has a moment of inertia (I) value of 414 in^4 and a section modulus (S) value of 36.2 in^3.
Before finalizing the size, additional checks like deflection, shear, and lateral-torsional buckling should also be performed.
Note: It is highly recommended to consult a qualified structural engineer to ensure the beam design is accurate and meets all safety requirements.
To design a simple beam for flexure, we need to determine the maximum moment and determine the required section modulus. We'll follow the basic steps to find the design requirements for the given beam:
Step 1: Calculate the total factored load (TFL)
The total factored load is calculated by combining the dead load (DL) and live load (LL) with appropriate load factors. Typically, the load factors are 1.2 for dead load and 1.6 for live load.
TFL = (DL * DL Load Factor) + (LL * LL Load Factor)
In this case,
DL = 13.2 kips (uniformly distributed dead load)
LL = 26.4 kips (uniformly distributed live load)
DL Load Factor = 1.2
LL Load Factor = 1.6
TFL = (13.2 * 1.2) + (26.4 * 1.6)
Step 2: Determine the maximum moment (Mmax)
The maximum moment occurs at the center of the beam under uniformly distributed load. The formula to calculate the maximum moment is:
Mmax = (TFL * L^2) / 8
In this case,
L = 14 ft (length of the beam)
Mmax = (TFL * L^2) / 8
Step 3: Calculate the required section modulus (S)
The required section modulus is calculated using the formula:
S = (Mmax * 12) / Allowable Stress
The allowable stress depends on the type of material used for the beam. For example, if it's steel, the typical allowable stress can be 24 ksi.
S = (Mmax * 12) / Allowable Stress
By following these steps, you can now calculate the total factored load, maximum moment, and the required section modulus for the given beam.