Page 198 - Handbook of Civil Engineering Calculations, Second Edition

HANGERS, CONNECTORS, AND WIND-STRESS ANALYSIS 1.181

Calculation Procedure:

1. Compute the required area of the base plate; establish the plate
dimensions
Refer to the base-plate diagram in the AISC Manual. The column load is assumed to be
uniformly distributed within the indicated rectangle, and the footing reaction is assumed
to be uniformly distributed across the base plate. The required thickness of the plate is es-
tablished by computing the bending moment at the circumference of the indicated rectan-
gle. Let f maximum bending stress in plate; p bearing stress; t thickness of plate.
The ACI Code permits a bearing stress of 750 lb/sq.in. (5170.5 kPa) if the entire con-
crete area is loaded and 1125 lb/sq.in. (7755.8 kPa) if one-third of this area is loaded. Ap-
plying the 750-lb/sq.in. (5170.5-kPa) value, we get plate area load, lb/750
2
240,000/750 320 sq.in. (2064.5 cm ).
The dimensions of the W14 53 are d 13.94 in. (354.3 mm); b 8.06 in. (204.7 mm);
0.95d 13.24 in. (335.3 mm); 0.80b 6.45 in. (163.8 mm). For economy, the projections m
and n should be approximately equal. Set B 15 in. (381 mm) and C 22 in. (558.8 mm);
2
then, area 15(22) 330 sq.in. (2129 cm ); p 240,000/330 727 lb/sq.in. (5011.9 kPa).
2. Compute the required thickness of the base plate
1
Thus, m /2(22 – 13.24) 4.38 in. (111.3 mm), which governs. Also, n /2(15 – 6.45)
1
4.28 in. (108.7 mm).
The AISC Specification permits a bending stress of 27,000 lb/sq.in. (186.1 MPa) in a
2 2
rectangular plate. The maximum bending stress is f M/S 3pm /t ; t m(3p/f ) 0.5
4.38(3 727/27,000) 0.5 1.24 in. (31.5 mm).
3. Summarize the design
1
Thus, B 15 in. (381 mm); C 22 in. (558.8 mm); t 1 /4 in. (31.8 mm).

BASE FOR STEEL COLUMN
WITH END MOMENT

A steel column of 14-in. (355.6-mm.) depth transmits to its footing an axial load of 30 kips
(133.4 kN) and a moment of 1100 in.·kips (124.3 kN·m) in the plane of its web. Design the
base, using A307 anchor bolts and 3000-lb/sq.in. (20.7-MPa) concrete.

Calculation Procedure:

1. Record the allowable stresses and modular ratio
Refer to Fig. 12. If the moment is sufficiently large, it causes uplift at one end of the plate
and thereby induces tension in the anchor bolt at that end. A rigorous analysis of the
stresses in a column base transmitting a moment is not possible. For simplicity, compute
the stresses across a horizontal plane through the base plate by treating this as the cross
section of a reinforced-concrete beam, the anchor bolt on the tension side acting as the re-
inforcing steel. The effects of initial tension in the bolts are disregarded.
1
The anchor bolts are usually placed 2 /2 (63.5 mm) or 3 in. (76.2 mm) from the column
flange. Using a plate of 26-in. (660-mm) depth as shown in Fig. 12a, let A s anchor-bolt
cross-sectional area; B base-plate width; C resultant compressive force on base plate;
T tensile force in anchor bolt; f s stress in anchor bolt; p maximum bearing stress;
p
bearing stress at column face; t base-plate thickness.