Chapter 5 Spread footing design
Chapter 5 Spread footing design
5.1 Footings:classification and purpose A footing carrying a single column is called a spread footing,since its function is to "spread" the column load laterally to the soil so that the stress intensity is reduced to a value that the soil can safely carry. Spread footings with tension reinforcing may be called two-way or one-way depending on whether the steel used for bending runs both ways or in one direction. Single footings may be of constant thickness or either stepped or sloped. Figure 5.1-the types of spread footing 园
5.1 Footings: classification and purpose ▪ A footing carrying a single column is called a spread footing, since its function is to “spread” the column load laterally to the soil so that the stress intensity is reduced to a value that the soil can safely carry. ▪ Spread footings with tension reinforcing may be called two-way or one-way depending on whether the steel used for bending runs both ways or in one direction. ▪ Single footings may be of constant thickness or either stepped or sloped. ▪ Figure 5.1-the types of spread footing
5.2 Allowable soil pressures in spread footing design The allowable soil pressure for footing design is obtained as the worst case of bearing capacity and settlement. The footing loads may consist of a combination of vertical and horizontal loads (inclined resultant)or these loads in combination with overturning moment. The safety factor ranges from 2 to 5 for cohesionless materials or from 3 to 6 for cohesive materials. The allowable bearing pressure may no be found using the B
5.2 Allowable soil pressures in spread footing design ▪ The allowable soil pressure for footing design is obtained as the worst case of bearing capacity and settlement. ▪ The footing loads may consist of a combination of vertical and horizontal loads (inclined resultant) or these loads in combination with overturning moment. ▪ The safety factor ranges from 2 to 5 for cohesionless materials or from 3 to 6 for cohesive materials. ▪ The allowable bearing pressure may no be found using the B’
5.3 Assumption used in footing design Theory of elasticity analysis and observations indicate that the stress distribution beneath symmetrically loaded footing is not uniform. ■ The actual stress distribution depends on both footing rigidity and base soil. The pressure distribution beneath most footings will be rather indeterminate because of the interaction of the footing rigidity with the soil type,state,and time response to stress. ◆ For this reason it is common practice to use the linear pressure distribution beneath spread footings
5.3 Assumption used in footing design ▪ Theory of elasticity analysis and observations indicate that the stress distribution beneath symmetrically loaded footing is not uniform. ▪ The actual stress distribution depends on both footing rigidity and base soil. ▪ The pressure distribution beneath most footings will be rather indeterminate because of the interaction of the footing rigidity with the soil type, state, and time response to stress. ▪ For this reason it is common practice to use the linear pressure distribution beneath spread footings
5.4 Rectangular footings Rectangular footings are necessary where an overturning moment is present to produce a more economical footing. The depth will be controlled by shear,except that wide- beam action will probably control if the L/B ratio is much greater than 1 or where an overturning moment is present. The placement of the reinforcement. Steel in the short direction is usually placed on the top of the longitudinal steel for some savings in mass and placing. Since the footing zone in the column area is more effective in resisting bending,a specified percentage of the total short-side steel is placed in this zone
5.4 Rectangular footings ▪ Rectangular footings are necessary where an overturning moment is present to produce a more economical footing. ▪ The depth will be controlled by shear, except that widebeam action will probably control if the L/B ratio is much greater than 1 or where an overturning moment is present. ▪ The placement of the reinforcement. ▪ Steel in the short direction is usually placed on the top of the longitudinal steel for some savings in mass and placing. ▪ Since the footing zone in the column area is more effective in resisting bending, a specified percentage of the total short-side steel is placed in this zone
5.5 Eccentrically loaded spread footings When footings have overturning moments as well as axial loads,the resultant soil pressure does not coincide with the centroid of the footing. If we assume the footing is somewhat less than rigid,the application of the static equation give a triangular soil pressure and displacement zone. The eccentrically loaded spread footing should be designed by using dimension B',L'. The center of the resultant uniform soil pressure is at the centroid of the B',L'rectangle
5.5 Eccentrically loaded spread footings ▪ When footings have overturning moments as well as axial loads, the resultant soil pressure does not coincide with the centroid of the footing. ▪ If we assume the footing is somewhat less than rigid, the application of the static equation give a triangular soil pressure and displacement zone. ▪ The eccentrically loaded spread footing should be designed by using dimension B’, L’. ▪ The center of the resultant uniform soil pressure is at the centroid of the B’, L’ rectangle
5.5 Eccentrically loaded spread footings By using dimensions of at least Bmin and Lmin the rectangular pressure zone will always include the column. This allows us to take the moment arms for tension steel on the pressed side,giving for the minimum values of B'and L'moment arms of length Ly=B'-Wy Lx=L'-Wx The amount of steel computed for a unit width is used across the full base dimensions of B and L. For two-way shear we have two options:①~②
5.5 Eccentrically loaded spread footings ▪ By using dimensions of at least Bmin and Lmin the rectangular pressure zone will always include the column. ▪ This allows us to take the moment arms for tension steel on the pressed side, giving for the minimum values of B’ and L’ moment arms of length ▪ Ly=B’-wy Lx=L’-wx ▪ The amount of steel computed for a unit width is used across the full base dimensions of B and L. ▪ For two-way shear we have two options:①～②
5.5 Eccentrically loaded spread footings It should be evident that a column can transmit a moment to the footing only if it is rigidly attached. Any footing rotation reduces the moment M applied to the footing with a corresponding 得 change to the far-end moment M;on the column. 志 A sufficiently large rotation can reduce moment to zero(depends on the El/Lc of the column)
5.5 Eccentrically loaded spread footings ▪ It should be evident that a column can transmit a moment to the footing only if it is rigidly attached. ▪ Any footing rotation reduces the moment Mf applied to the footing with a corresponding change to the far-end moment Mf ’ on the column. ▪ A sufficiently large rotation can reduce moment to zero (depends on the EIc /Lc of the column)
5.5 Eccentrically loaded spread footings For eccentrically out of the middle 1/3 of a L/2=e+L'/3 footing,a method used by many structural designers r(a) assumes a triangular 1 3B(L/2-e) ≤qa pressure distribution. 喝 周 超
5.5 Eccentrically loaded spread footings ▪ For eccentrically out of the middle 1/3 of a footing, a method used by many structural designers assumes a triangular pressure distribution. ( ) ( ) − = = = + qa B L e P q BL q P L e L 3 / 2 2 2 / 2 / 3
