5.5-5 The beam shown in Figure P5.5-5 is a two-span beam with a pin (hinge) in the center of the left span, making the beam statically determinate. There is continuous lateral support. The concentrated loads are service live loads. Determine whether a W18 × 60 of A992 steel is adequate. a. Use LRFD.
5.5-5 The beam shown in Figure P5.5-5 is a two-span beam with a pin (hinge) in the center of the left span, making the beam statically determinate. There is continuous lateral support. The concentrated loads are service live loads. Determine whether a W18 × 60 of A992 steel is adequate. a. Use LRFD.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Would a W18X 60 steel beam of A992 steel work for the figure shown.
![### Structural Engineering Analysis: Beam Load Evaluation
**Problem 5.5-5a**
**Objective:**
Determine if a W18x60 A992 beam is adequate for given concentrated live loads.
**Assumptions:**
- Don't account for self-weight (based on class instructions).
- Yield strength (Fy) = 50 ksi.
**Beam Load Configuration:**
- **Position A:** 12 kips
- **Position B:** 8 kips
- **Position D:** 8 kips
Load calculations:
- \( P_1 = (1.6)(12k) = 19.2k \)
- \( P_2 = (1.6)(8k) = 12.8k \)
- \( P_3 = (1.6)(8k) = 12.8k \)
**Diagrams:**
1. **Beam Diagram:**
- Displays the beam with three points of concentrated loads at intervals of 28 feet, with supports at points A and D.
2. **Load Distribution:**
- Cross-section showing concentrated loads as point loads at the beam's length.
**Calculations:**
1. **Flange Slenderness:**
- \(\lambda = 5.44\)
- \(\frac{0.38}{F_y} = 9.15 = \lambda_p\)
- Result: Compact
2. **Web Slenderness:**
- \(\lambda = 38.7\)
- \(\frac{3.76}{F_y} = 90.55\)
- Result: Compact
3. **Moment Capacities:**
- \[
M_n = M_p = F_yZ_x
\]
- \( Z_x = 123 \text{ in}^3 \)
- \[
M_n = (50 \text{ ksi})(123 \text{ in}^3) = 6150 \text{ kip-in} = 512.5 \text{ kip-ft}
\]
- \[
\phi M_n = 0.9 \times (512.5 \text{ kip-ft}) = 461.25 \text{ kip-ft}
\]
**Conclusion:**
- The design strength (\(\phi M_n\)) of the W18x60 beam is 461.25 kip](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc4000f3-d001-4353-9cb7-6c40ac56fbbe%2Fe89dfe77-04df-47df-893f-89333a36b8db%2F4i8fzsr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Structural Engineering Analysis: Beam Load Evaluation
**Problem 5.5-5a**
**Objective:**
Determine if a W18x60 A992 beam is adequate for given concentrated live loads.
**Assumptions:**
- Don't account for self-weight (based on class instructions).
- Yield strength (Fy) = 50 ksi.
**Beam Load Configuration:**
- **Position A:** 12 kips
- **Position B:** 8 kips
- **Position D:** 8 kips
Load calculations:
- \( P_1 = (1.6)(12k) = 19.2k \)
- \( P_2 = (1.6)(8k) = 12.8k \)
- \( P_3 = (1.6)(8k) = 12.8k \)
**Diagrams:**
1. **Beam Diagram:**
- Displays the beam with three points of concentrated loads at intervals of 28 feet, with supports at points A and D.
2. **Load Distribution:**
- Cross-section showing concentrated loads as point loads at the beam's length.
**Calculations:**
1. **Flange Slenderness:**
- \(\lambda = 5.44\)
- \(\frac{0.38}{F_y} = 9.15 = \lambda_p\)
- Result: Compact
2. **Web Slenderness:**
- \(\lambda = 38.7\)
- \(\frac{3.76}{F_y} = 90.55\)
- Result: Compact
3. **Moment Capacities:**
- \[
M_n = M_p = F_yZ_x
\]
- \( Z_x = 123 \text{ in}^3 \)
- \[
M_n = (50 \text{ ksi})(123 \text{ in}^3) = 6150 \text{ kip-in} = 512.5 \text{ kip-ft}
\]
- \[
\phi M_n = 0.9 \times (512.5 \text{ kip-ft}) = 461.25 \text{ kip-ft}
\]
**Conclusion:**
- The design strength (\(\phi M_n\)) of the W18x60 beam is 461.25 kip
Transcribed Image Text:### Structural Engineering - Load and Resistance Analysis
#### Problem Analysis
**Figure P5.5-4 Description:**
The beam depicted in this figure is a two-span beam with a hinge located at the center of the left span. This hinge creates a statically determinate structure. The beam bears concentrated service live loads at specified points along its length.
Key Features:
- A pin (hinge) is placed in the center of the left span of the beam.
- The beam receives continuous lateral support.
- The loads applied to the beam are service live loads.
- The task is to determine whether a W18 x 60 of A992 steel is adequate for this beam.
**Task:**
Use Load and Resistance Factor Design (LRFD) to evaluate the beam's sufficiency.
---
#### Load Diagram
**Figure P5.5-5 Description:**
The diagram represents a beam with several specified sections and point loads.
**Dimensions and Load Details:**
- The beam is composed of two spans divided into segments of 28 feet and 14 feet on either side of each support.
- Vertical point loads are applied at specific points:
- 12 kips at point A on the first span.
- 8 kips at point B on the second span.
- 8 kips again at points C and D.
**Support Conditions:**
- A roller support is at point A.
- A pin support (hinge) at the midpoint between sections A and C.
- Both ends of the beam are supported, creating a stable structure with defined reaction points.
This configuration provides insight into load distribution and support reactions within the beam system. The analysis would involve calculating moment distributions, shear forces, and deflections to ensure compliance with structural engineering standards.
#### Additional Information
**Section 5.5.6:**
Discusses the use of a W12 x 30 of A992 steel, with emphasis on unbraced length and other critical design parameters. Calculation requirements using specific coefficients are also described for enhanced structural integrity.
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