Introduction to Masonry Beams
General Discussion | Behavior | Adapt to Reinforced Masonry Beams
- A masonry beam is composed of solidly grouted units reinforced with steel.
- It is often called a lintel when spanning over openings in walls.
- The design method used here is Working Stress Design (WSD). Its relationship to
other methods used in masonry is shown in the following stress-strain figure.
- WSD assumptions:
- Plane secions remain plane during and after bending.
- s is proportional to e
- e is proportional to the distance from n.a.
- Masonry is cracked:
- It carries no tensile stresses.
- Reinforcing steel resists tension.
- Masonry resists compressive stresses only
- Design stresses within elastic range.
- Perfect bond between steel and grout.
Behavior in Bending - A Review
- During the bending deformation of a simply-supported beam:
- Upper fibers shorten due to axial compression
- Lower fibers lengthen due to axial tension
- Fiber at n.a. => No Deformation => No Strain
- More Deformation => More Strain => More Stress
- Generic distribution of stress across the cross section of a beam:
- Stresses act normal to cross section.
- These axial stresses are induced by bending that is quantified in terms of the
internal bending moment, M.
- M = Ca = Ta
- Where M is the internal force couple (i.e. bending moment) that resists the externally generated M which is a function of span, support conditions, and loads.
Adapt to Reinforced Masonry Beams
- Reinforced masonry beams are orthotropic.
- Recall the WSD assumptions: masonry resists compression and steel resists tension.
- In effect, this means that we assume that the masonry beam is cracked below the n.a. and cannot resist any tension.
- This really isn't true under working loads, and therefore results in a large safety margin.
- But, the uncertainty of measuring tensile stress in masonry necessitates this.
- The modified stress distribution for reinforced masonry bending member:
- Because we assume a perfect bond between steel and grout:
- Strain in steel = strain in grout at corresponding location.
- With this assumption we can transform the masonry-steel section into a section of one material: masonry.
- Transform the steel into an equivalent masonry area by multiplying As by n, the modular ratio.
n = Es / Em
where Es = 29 x 10 6 psi, and
Em = 750 (f ` m) £ 3 x 10 6 for concrete unit masonry.- for additional information on modulus of elasticity, see UBC ' 97 2106.2.12
- The resultant compressive force can be found from essentially a volume calculation:
F = s A = 1/2 fm ( k d ) b = C
- Likewise, the resultant tensile force is:
F = s A = (fs / n) (n As) = As fs
- The internal resisting bending moment is then:
M = Ca = Ta, but a = j d for reinforced masonry beams, and
M = 1/2 fm k j b d2 or M = As fs j d.
