Structural Masonry Design Examples

Material Properties

Example 1 - Calculating the Thermal Stress and Strain for a Reinforced Concrete Masonry Wall Experiencing Temperature Variation

For a concrete masonry wall constructed from nominal 8 x 8 x 16 in. medium-weight units with the following parameters:

 

Length of Wall – 30 ft
Height of Wall – 15 ft
Grout Weight – 140 lbs/ft^3, wall is fully grouted
28 Day Compressive Strength of Masonry – 2000 lb/in^2
Temperature in local area varies from 75 degrees Fahrenheit to 125 degrees Fahrenheit

 

Calculate

A. The amount of thermal movement the wall would experience due to temperature variation
B. The induced stress in the wall if the thermal movement is restrained

Example 2 - Calculating the Deformation and Stress for a Reinforced Concrete Masonry Wall Undergoing Shrinkage

For a concrete masonry wall constructed from nominal 8 x 8 x 16 in. medium-weight units with the following parameters:

 

Length of Wall – 30 ft
Height of Wall – 15 ft
Grout Weight – 140 lbs/ft^3, wall is fully grouted
28 Day Compressive Strength of Masonry – 2000 lb/in^2

 

Calculate

A. The total shrinkage in the concrete masonry wall
B. The maximum stress that would be induced if the shrinkage movement is prevented

Flexural Analysis of Beams

Example 1 - Calculating the Depth of the Compressive Stress Block, Location of Neutral Axis, and Tensile Strain for a Reinforced Concrete Masonry Beam

The nominal 10 in x 40 in reinforced concrete masonry beam shown below has the following parameters:

 

Reinforcement – (2) #6 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 40 inches
Effective Depth, d – 34 inches
Compressive Strength of Masonry, f’m – 1500 psi

 

Calculate:

A. The depth of the compressive stress block, “a”
B. Location of the neutral axis, “c”
C. Tensile strain in the steel reinforcement

Example 2 - Checking the Adequacy of a Reinforced Concrete Masonry Beam Subjected to Dead and Live Loads per ACI 530-11

The nominal 10 in x 40 in reinforced concrete masonry beam built from lightweight CMU shown below has the following parameters:

 

Reinforcement – (2) #6 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 40 inches
Effective Depth, d – 34 inches
Compressive Strength of Masonry, f’m – 1500 psi
Span Length – 16 ft
Service Live Load – 2000 lbs/ft
Grout Weight – 140 lbs/ft^3
Self-Weight – 93 lbs/ft^2

 

Check the adequacy of the beam for the given service loads

 

Example 3 - Calculating the Design Flexural Strength of a Reinforced Concrete Masonry Beam per ACI 530-11

The nominal 8 in x 24 in reinforced concrete masonry beam shown below has the following parameters:

 

Reinforcement – (1) #7 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 24 inches
Effective Depth, d – 20 inches
Compressive Strength of Masonry, f’m – 2000 psi
Assume Mu/Vu*dv is greater than or equal to 1

 

Compute the design moment strength for the beam

Example 4 - Calculating the Design Flexural Strength of a Reinforced Clay Masonry Beam per ACI 530-11

The two-wythe 8 in x 24 in clay brick beam shown below has the following parameters:

 

Reinforcement – (1) #8 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 24 inches
Effective Depth, d – 20 inches
Compressive Strength of Masonry, f’m – 2000 psi

 

Assume Mu/Vu*dv is greater than or equal to 1, and Portland cement Type S mortar will be used for construction

 

Compute the design moment strength for the beam

Example 5 - Calculating the Design Flexural Strength of a Reinforced Concrete Masonry Beam Using the Steel Ratio and Reinforcing Index

The nominal 10 in x 40 in reinforced concrete masonry beam built from lightweight CMU shown below has the following parameters:

 

Reinforcement – (2) #6 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 40 inches
Effective Depth, d – 34 inches
Compressive Strength of Masonry, f’m – 1500 psi
Span Length – 16 ft
Service Live Load – 2000 lbs/ft
Grout Weight – 140 lbs/ft^3
Self-Weight – 93 lbs/ft^2

 

Check the adequacy of the beam for the given service loads

Example 6 - Calculating the Uniform Dead and Live loads that a Reinforced Concrete Masonry Beam Can Carry

The nominal 8 in x 24 in reinforced concrete masonry beam shown below has the following parameters:

 

Reinforcement – (1) #7 bars
Yield Strength of Reinforcement, Fy – 60 ksi
Total Depth, h – 24 inches
Effective Depth, d – 20 inches
Compressive Strength of Masonry, f’m – 2000 psi
Dead-to-Live Load Ratio – 0.7
Span Length – 12 feet

 

Assume Mu/Vu*dv is greater than or equal to 1

 

Find the uniform service live load and dead load that the beam can safely carry