Handbook of Civil Engineering Calculations

Calculation Procedure:

1. Compute the unit loads W 1 , W 2 , and W 3
   Refer to the AISC Specification and Manual. Although ostensibly we apply the elastic-
   stress method, the design of a composite steel-and-concrete beam in reality is based on
   the ultimate-strength behavior of the member. Loads that are present before the concrete
   has hardened are supported by the steel member alone; loads that are present after the
   concrete has hardened are considered to be supported by the composite member, regard-
   less of whether these loads originated before or after hardening. The effects of plastic
   flow are disregarded.
   The subscripts 1, 2, and 3 refer, respectively, to dead loads applied before hardening
   of the concrete, dead loads applied after hardening of the concrete, and live loads. The
   subscripts b, ts, and tc refer to the bottom of the member, top of the steel, and top of the
   concrete, respectively. The superscripts c and n refer to the composite and noncomposite
   member, respectively.
   We compute the unit loads for a slab weight of 63 Ib/lin ft (0.92 kN/m) and an as-
   sumed steel weight of 80 Ib/lin ft (1167.5 N/m): W 1 = 63(11) + 80 = 773 Ib/lin ft (11.3
   kN/m); W 2 = 30(11) = 330 Ib/lin ft (4.8 kN/m); W 3 = 200(11) = 2200 Ib/lin ft (32.1 kN/m).


2. Compute all bending moments required in the design
   Thus, M 1 = 12[(%)0.773(36)^2 + '/4(10)36] = 2583 in-kips (291.8 kN-m); M 2 =
   0/8)0.330(36)^212 = 642 in-kips (72.5 kN-m). M 3 = (%)2.200(36)^212 = 4277 in-kips (483.2
   kN-m); Mc = 2583 + 642 + 4277 = 7502 in-kips (847.6 kN-m); M* = 2583 in-kips (291.8
   kN-m); MDL = 2583 + 642 = 3225 in-kips (364.4 kN-m); M1x = 4277 in-kips (483.2
   kN-m).


3. Compute the required section moduli with respect to the steel,
   using an allowable bending stress of 24 kips/in^2 (165.5 MPa)
   In the composite member, the maximum steel stress occurs at the bottom; in the noncom-
   posite member, it occurs at the top of the steel if a bottom-flange cover plate is used.
   Thus, composite section, Sb = 7502/24 = 312.6 in^3 (5122.6 cm^3 ); noncomposite sec-
   tion, Sts = 2583/24 = 107.6 in^3 (1763.3 cm^3 ).


4. Select a trial section by tentatively assuming that the
   composite-design tables in the AISC Manual are applicable
   The Manual shows that a composite section consisting of a 5-in (127-mm) concrete slab,
   a Wl 8 x 55 steel beam, and a cover plate having an area of 9 in^2 (58.1 cm^2 ) provides Sb =
   317.5 in^3 (5202.9 cm^3 ). The noncomposite section provides Sts = 113.7 in^3 (1863.2 cm^3 ).
   Since unshored construction is to be used, the section must conform with the Manual
   equation 1.35 + 0.35MLL/MDL = 1.35 + 0.35(4277/3225) = 1.81. AndSg/Sff = 317.5/213.6
   = 1.49, which is satisfactory.
   The flange width of the W18 x 55 is 7.53 in (191.3 mm). The minimum allowable dis-
   tance between the edge of the cover plate and the edge of the beam flange equals the size
   of the fillet weld plus^5 /i6 in (7.9 mm). Use a 9 x 1 in (229 x 25 mm) plate. The steel sec-
   tion therefore coincides with that presented in the AISC Manual, which has a cover plate
   thickness tp of 1 in (25.4 mm). The trial section is therefore Wl 8 x 55; cover plate is 9 x 1
   in (229 x 25 mm).


5. Check the trial section
   The AISC composite-design tables are constructed by assuming that the effective flange
   width of the member equals 16 times the slab thickness plus the flange width of the steel.
   In the present instance, the effective flange width, as governed by the AISC, is^1 AL =
   !/4(36)12 = 108 in (2743 mm); spacing of beams = 132 in (3353 mm); 16/ + 7.53 = 16(5) +
   7.53 = 87.53 in (2223.3 mm), which governs.