A Beginner's Guide to ACI 318-14

Chapter 3 - Strength Analysis

© 2018 T. Bartlett Quimby

Section 3.7

Homework Problems

Last Revised: 04/08/2018

The homework problems in the chapter are all hypothetical analysis problems. They are intended to help reinforce the basic principles of strain compatibility and equilibrium. A thorough understanding of these concepts will make it possible to deal with a wide variety of practical design problems in later chapters.

Miscellaneous Problems

Problems M3.1:  Use the section drawing MISCDET_Conc 1/S1.1 and the following parameters for this problem:

• f’_c = 3,500 psi
• f_y = 60,000 psi
• Bar Size: #10

For the given section and parameters, show that:

Problem M3.1.1: -P_nmax = -1,935 kips

Problem M3.1.2: For bending about the "X" axis:

Problem M3.1.3: For bending about the "Y" axis:

Problem M3.1.4: +P_nmax = 533 kips

Problems M3.2:  Use the section drawing MISCDET_Conc 1/S1.1 and the following parameters for this problem:

• f’_c = 3,500 psi
• f_y = 60,000 psi
• Bar Size: #10

For the given section and parameters, show that:

Problem M3.2.1: The pure bending capacity of the section about the "X" axis, M_nx = 377 ft-k.

Problem M3.2.2: The pure bending capacity of the section about the "Y" axis, M_ny = 492 ft-k.

Problem M3.2.3: The location of the neutral axis for the balanced condition for bending about the "X" axis, c_bx = 11.84 in. and that P_bx = -534 kips, M_bx = 490 ft-kips

Problem M3.2.4: Explain the significance of the balanced condition?

Problems M3.3:  Use the section drawing MISCDET_Conc 2/S1.1 and the following parameters for this problem:

• f’_c = 6,000 psi
• f_y = 40,000 psi
• Bar Size: #14

For the given section and parameters, show that:

Problem M3.3.1: When P_n = 0 and M_nx =0 ft-k that M_ny = 234 ft-k. (This is pure bending about the y axis.)

Problem M3.3.2: When P_n = 0 and M_ny =0 ft-k that M_nx = 231 ft-k (This is pure bending about the x axis.)

Problem M3.3.3: P_n = -1239 k, M_nx = 207 ft-k, and M_ny = 358 ft-k for e = 4" at 60 degrees (see drawing) from the horizontal axis.

Problem M3.3.4: -P_nmax = -2222 k and +P_nmax = 360 k.

Problem M3.4: Develop an Excel spreadsheet to compute and display the interaction curve for bending about the strong axis for a rectangular reinforced section as shown MISCDET_Conc 4/S1.1. The computation should consider any dimensions, concrete strength, steel strength, areas of steel, and location of steel. The output should identify the maximum tensile and compressive strengths, the pure bending strength, and the axial & flexural strength combination for the balanced condition.