Derivation of Live Load Conversions on Two-Way Slabs
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Question Bank: q313
PSAD - Structural Theory / Transmission of Loads / Engr. Janclyde Espinosa (Clidez)
The floor of a building shown is subjected to the following loads: Superimposed dead load = 2.4kPa Superimposed live load = 5.2kPa
AB, CD, EF and GH: W 250 x 115 kg/m ( WEIGHT = 115 kg/m )
AG and GH: W 310 x 74 kg/m
Concrete Slab thickness = 110 mm
Unit weight of concrete = 23.54 kN/m3
Compute the reaction at C and D, in kN, on beam CD.
66.11
33.74
59.64
46.12
Compute the reaction at A and B in kN, on beam AB.
33.12
17.43
32.13
18.96
Compute the total concentrated service load in kN on the column at A.
141.854
70.927
148.154
79.720
### Transmission of slab loads
The slab dead load is $0.110(23.54)=2.589 \text{kPa}$. Add the $2.4 \text{kPa}$ superimposed dead load and the $5.2 \text{kPa}$ live load, then distribute the slab load by tributary area to the secondary and primary beams. Include the listed beam self-weights before taking simple-beam reactions.
This gives the end reaction on beam $CD$,
$$R_C=R_D=\boxed{66.11 \text{kN}},$$
and on beam $AB$,
$$R_A=R_B=\boxed{33.12 \text{kN}}.$$
Summing all tributary beam reactions delivered to column $A$ gives
$$\boxed{P_A=141.854 \text{kN}}.$$
Question Bank: q314
PSAD - Structural Theory / Transmission of Loads / Engr. Janclyde Espinosa (Clidez)
The floor of a building shown is subjected to the following loads: Superimposed dead load = 2.8kPa Superimposed live load = 6.0kPa
CD and EF: W 310 x 86 kg/m ( WEIGHT = 86 kg/m )
AB, GH, AG, and BH: W 310 x 97 kg/m
Concrete Slab thickness = 100 mm
Unit weight of concrete = 24 kN/m3
Compute the total uniformly distributed service load in kN/m on beam CD.
28.84
21
21.84
22.84
Compute the total uniformly distributed service load in kN/m on beam AB.
14.95
11.95
14
11.45
Compute the total concentrated service load in kN on the column at A.
134.93
173.04
104.70
128.64
### Uniform loads and column load
The slab service load is
$$0.100(24)+2.8+6.0=11.2 \text{kPa}.$$
Using the tributary widths shown, then adding the stated beam weights, gives
$$w_{CD}=\boxed{28.84 \text{kN/m}},\qquad w_{AB}=\boxed{14.95 \text{kN/m}}.$$
Transfer the simple-beam end reactions from the framing into column $A$ to obtain
$$\boxed{P_A=134.93 \text{kN}}.$$
