Calculation of the Hanging Wall

Objective: Check of the load-bearing capacity of the hanging wall.

Task: Check the bearing strength of masonry above the support of the foundation beam.

References: Bedov A. I., Schepetieva T. A., Design of masonry and reinforced masonry constructions, Moskow : ASV publisher, 2003, p. 228

Compliance with the codes: SNiP II-22-81, SP 15.13330.2012.

Initial data file:
Example 15.SAV;
ComeIn.doc — report

Initial data:

The hanging wall without openings 7,2 m high and 0,8 m thick  is supported on the foundation reinforced concrete beam 0,38х0,42 (h) from heavy-weight natural hardening concrete of class В15 (E_b = 23 000 MPa). The distance between the supports of the beam is 6,0 m, the width of a support is 0,9 m.

The wall is made of molded clay brick of grade 75 with regular cement mortar of grade 25. The design resistance of masonry for compression is R = 1,3 MPa, the temporary resistance of masonry for compression is R_u = kR = 2×1,3 = 2,6 MPa. The elastic characteristic of masonry is α = 1000. The deformation modulus of masonry is E = 0,5E₀ = 0,5αR_u = 0,5×1000×2,6 = 1300 MPa.

Analytical solution:

The design beam support reaction without taking into account the load from its self-weight is equal to

N = 0,38×7,2×18×1,1×(6+2×0,45)/2 = 186,89 кН

Moment of inertia of the beam

\[ I=\frac{bh^{3}}{12}=\frac{0,38\cdot 0,42^{3}}{12}=0,002346 \quad м^{4}. \]

The height of the conventional chord with the equivalent rigidity is determined according to the following formula

\[ H_{0} =2\cdot \sqrt[3]{\frac{0,85E_{b} I}{E\cdot b}}=2\cdot \sqrt[3]{\frac{0,85\cdot 23000\cdot 0,002346}{1300\cdot 0,38}}=0,905м \]

The length of the base of the pressure distribution diagram

\[ l_{c} =a_{1} +0,8H_{0} =0,43+0,9\times 0,905\quad =\quad 1,2445 \quad м. \]

Bearing area

\[ A_{c} =1,2445\times 0,38\quad =\quad 0,473 м^{2}. \]

Design bearing resistance of the masonry

\[ R_{c} =\xi R=1,0\times 1,3\quad =\quad 1,3 МПа \]

Bearing strength of the masonry

\( N_{c} =\psi dR_{c} A_{c} =\psi (1,5-0,5\psi )R_{c} A_{c} =0,5 х1,25х1,3х0,473 = 384,3 кН > N= 186,89 \quad кН \), i.e. the strength of the masonry is provided.

 

COMEIN initial data

Importance factor  γ_n = 1

Age of masonry - up to a year
Working life is 25 years
Stone/brick - Molded clay brick
Stone/brick grade - 75
Mortar - regular cement with mineral plasticizers
Mortar grade - 50

Supporting beam

Reinforced concrete beam
Single-span

Concrete Concrete type: Heavy-weight Concrete class: B15 Density of concrete 2,5 T/m3 Hardening conditions: Natural Hardening factor 1

Structure

Design load per running meter of the wall q = 0,001 T/m Specific weight of masonry 1,8 T/m3 Hw = 7,2 m Bw = 0,38 m L = 6 m Bsup = 0,9 m

Comparison of solutions:

Check	Bearing strength of masonry above the support of the foundation beam
Manual	186,89/384,3 = 0,486
COMEIN	0,465
Deviation, %	3,6 %