Chapter 9, Problem 9.1.1P

BuyFind*arrow_forward*

6th Edition

Segui + 1 other

ISBN: 9781337094740

Textbook Problem

A
*b* of 81 inches. Sufficient anchors are provided to make the beam fully composite. The 28-day compressive strength of the concrete is

**a**. Compute the moment of inertia of the transformed section.

**b**. For a positive service load moment of 290 ft-kips, compute the stress at the top of the steel (indicate whether tension or compression), the stress at the bottom of the steel, and the stress at the top of the concrete.

To determine

**(a)**

The moment of inertia of the transformed section.

Answer

Explanation

**Given:**

A W 18 X 40 floor beam, the 28-day compressive strength of the concrete is

**Calculation:**

We have the modulus of elasticity of concrete as follows:

Where, the modulus of elasticity of concrete is

unit weight of concrete is

the 28-day compressive strength of concrete is

Substitute

Modular ratio by using the following formula:

Where, the modulus of elasticity of concrete is

the modulus of elasticity of steel is

and n is the modular ratio.

Substitute

Now the section will be transformed.

Since the modulus of elasticity of concrete can only be approximated, the usual practice of rounding n to the nearest whole number is sufficiently accurate. Thus,

The transformed width of the section is as following:

Where,

Substitute

Following is the section for the given set of conditions:

Data from the steel code:

DesignationImperial (in x lb/ft) |
Depthh (in) |
Widthw (in) |
Web Thicknesst_{w} (in) |
Flange Thicknesst_{f} (in) |
Sectional Area (in^{2}) |
Weight (lb_{f}/ft) |
Static Parameters |
|||

Moment of Inertia |
Elastic Section Modulus |
|||||||||

I_{x} (in^{4}) |
I_{y} (in^{4}) |
S_{x} (in^{3}) |
S_{y} (in^{3}) |
|||||||

W 18 x 40 | 17.9 | 6.02 | 0.315 | 0.525 | 11.8 | 40 | 612 | 19.1 | 68.4 | 6.4 |

The transformed section is shown in the above figure. The neutral axis is not known yet whether it lies in the steel or the concrete.

The location of the neutral axis can be found by applying the principle of moments with the axis of moments at the top of the slab. The computations are summarized in Table, and the distance from the top of the slab to the centroid is:

Component | |||

Concrete | |||

W 18 X 40 | |||

Sum |

The distance of centroid of the section is as follows:

Substitute

Since this is greater than 4 inches (the thickness of the slab) the neutral axis lies below the slab in the web. Applying the parallel axis theorem and tabulating the computations in table, we obtain the moment of inertia of the transformed section as:

Component | |||||

Concrete | |||||

W 18 X 40 | |||||

Sum |

**Conclusion:**

Therefore, total moment of inertia of the transformed section is

To determine

**(b)**

The stress at the top of the steel (indicate whether tension or compression), the stress at the bottom of the steel, and the stress at the top of the concrete.

Answer

Explanation

**Given:**

Positive service load moment of 290 ft-kips.

**Calculation:**

For the computation of the stress at top of the steel is as following:

Where, the stress at the top of the steel is

The distance from neutral axis to top of steel section is as follows:

Here the thickness of the concrete slab is t.

Compute the stress at top of the steel as:

As, the centroid lies below the top of the steel, the stress is compressive.

Now, the stress at the bottom of the steel is as follows:

The distance from the neutral axis to bottom of steel section.

Where,

As, the centroid lies above the top of steel, the stress is tensile.

Stress at the top of the slab is as follows:

Where, n is the modular ratio is n.

As the concrete slab is above the neutral axis, hence the stress is compressive.

**Conclusion:**

Therefore, the stress at top of steel section is

Ch-9 P-9.1.1PCh-9 P-9.1.2PCh-9 P-9.1.3PCh-9 P-9.1.4PCh-9 P-9.1.5PCh-9 P-9.1.6PCh-9 P-9.2.1PCh-9 P-9.2.2PCh-9 P-9.3.1PCh-9 P-9.3.2P

Ch-9 P-9.4.1PCh-9 P-9.4.2PCh-9 P-9.4.3PCh-9 P-9.4.4PCh-9 P-9.4.5PCh-9 P-9.5.1PCh-9 P-9.5.2PCh-9 P-9.5.3PCh-9 P-9.6.1PCh-9 P-9.6.2PCh-9 P-9.6.3PCh-9 P-9.6.4PCh-9 P-9.6.5PCh-9 P-9.7.1PCh-9 P-9.7.2PCh-9 P-9.7.3PCh-9 P-9.7.4PCh-9 P-9.8.1PCh-9 P-9.8.2PCh-9 P-9.8.3PCh-9 P-9.8.4PCh-9 P-9.8.5PCh-9 P-9.8.6PCh-9 P-9.8.7PCh-9 P-9.8.8PCh-9 P-9.8.9PCh-9 P-9.8.10PCh-9 P-9.10.1PCh-9 P-9.10.2P

Solid Waste Engineering

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

Principles of Geotechnical Engineering (MindTap Course List)

Fundamentals of Geotechnical Engineering (MindTap Course List)

Mechanics of Materials (MindTap Course List)

Database Systems: Design, Implementation, & Management

Management Of Information Security

Automotive Technology: A Systems Approach (MindTap Course List)

Fundamentals of Information Systems

Precision Machining Technology (MindTap Course List)

A Guide to SQL

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

Electric Motor Control

EBK ELECTRICAL WIRING RESIDENTIAL

Database Systems: Design, Implementation, & Management

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

International Edition---engineering Mechanics: Statics, 4th Edition

Fundamentals of Information Systems

Principles of Information Security (MindTap Course List)

Cornerstones of Financial Accounting

Principles of Information Systems (MindTap Course List)

Find all the answers to your study problems with bartleby.

Textbook solutions plus Q&A. Get As ASAP *arrow_forward*