Chen, W. F.

Siciliano, Michael

English

Lehigh University: Lehigh Preserve

Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1971
Bearing strength of concrete blocks, May 1971,
Special Topics report for M. S. degree for Siciliano
Michael Siciliano
W. F. Chen
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Siciliano, Michael and Chen, W. F., "Bearing strength of concrete blocks, May 1971, Special Topics report for M. S. degree for
Siciliano" (1971). Fritz Laboratory Reports. Paper 2027.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/2027
THE BEARrnG STRENGTH OF CONCRETE BLOCKS 
by 
M. Siciliano1 
and 
W. F. Chen2 
ABSTRACT 
An experimental investigation was made to ascertain the 
validity of the linear elastic and perfectly plastic solutions of 
the bearing capacity of concrete blocks with axially or eccentrically 
located ducts and axially or eccentrically loaded by two rigid punches. 
The results obtained showed that when the concrete in bearing 
is confined as in the concentrically loaded blocks, the plastic theory 
controlled, while in the case where there was little confinement, as in 
the eccentrically loaded blocks, the results were bounded by the plastic 
a~d the elastic solutions. 
1 Graduate Student, Department of Civil Engineering, Lehigh University, 
Bethlehem, Pennsylvania. 
3 Associate Professor of Civil Engineering, Fritz Engineering Lab-
oratory, Lehigh University, Bethlehem, Pennsylvania. 
-1-
1. INTRODUCTION 
The bearing capacity of concrete is of technical importance 
because of its frequent engineering applications, such as in foun-
dations and in post-tensioned concrete beams. The problem of end 
bearing in a post-tensioned concrete beam may be idealized and 
simplified to the problem (Fig. 1) of a circular cylindrical or a 
square prismatic concrete block with a longitudinal cable duct loaded 
by two circular or square punches applied on the cable duct at both 
ends. Bearing capacity solutions for the idealized problem were re-
cently presented in Ref. 1. Good experimental verifications of the 
solutions were available for the special case of concrete blocks 
with eccentricity but without cable duct. No suitable experimental 
data were available, however, for concrete blocks with both punch 
eccentricity and cable duct (Fig. 1). 
A typical stress-strain curve for concrete is shown in 
Fig. 2; it can be seen from the curve that concrete is an elastic-
plastic and fracture material. An elastic-plastic fracture solution 
to the bearing problem is difficult and at the present time probably 
not possible since the general stress-strain relationship for con-
crete in the inelastic range as well as the fracture criterion of 
concrete, which are required for such a solution, are not known. 
An approach to the problem is to idealize the concrete as 
linear elastic material (Fig. 2). This idealization has been used 
in previous solutions to this problem. Iyengar and Yogananda [2] 
-2-
and Nishibayashi, Kiyama, and Sakata [3] have done a complete three-
dimensional elastic solution for the axial symmetrical case, a circular 
punch on a circular cylindrical block with an axial cable duct. The 
three-dimensional solution of the case of a rectangular punch on a 
rectangular prism without a cable duct also has been reported re-
cently by Iyengar and Prabhakara [4]. It can be seen from the stress-
strain curve (Fig. 2) that the curve is only linear initially, and 
the greater the stress the greater the divergence from the linear 
elastic idealization. 
Another approach to this problem is to idealize the con-
crete as a linear-elastic perfectly plastic material (Fig. 2); this 
idealization has been developed and justified by Chen and Drucker 
for some bearing capacity problems [5] and was used recently by 
Chen and Covarrubias [1] to obtain numerical solutions to the bearing 
problem. The stress-strain curve (Fig. 2) shows that this idealization 
also diverges from the actual case. Concrete can be altered, however, 
to better approach the perfectly plastic plateau by increasing its 
tension ductility; this can be done, for example, by adding random 
wire reinforcement to the concrete, this has been reported by Carson 
and Chen [6,7]. 
The purpose of this paper is to test specimens with vari-
ations of duct diameters and eccentricities with both plain and random 
wire reinforced concrete. The test results will then be compared with 
the theoretical linear elastic and perfectly plastic solutions. 
-3-
·-
•-
2. EXPERIMENTAL WORK 
Scope 
A double punch test was used for all specimens; this con-
sisted of loading the block with two steel punches at opposite ends 
of the block (Fig. 1). Specimen diameters or edges and punch diameters 
or edges were constant at 6 and 1.5 inches, respectively, with heights 
of 9 or 6 inches. Specimens with eccentricitie~ of 0.75, 1.50, and 
2.25 inches and duct diameters of 0.25, 0.50, 0.875, and 1.25 inches 
were tested. 
Specimens 
All specimens were mixed and cast in accordance with ASTM 
Specification Cl92. The specimens with holes were cast with a steel 
rod placed in the mold, the rod was covered with form wax to facilitate 
removal. The rods were removed after 8 hours. The specimens were 
stripped after 48 hours and were placed in a 100% relative humidity 
curing room at about 75°F for 14 days, then are dried for 7 days before 
testing. 
Materials 
The plain concrete mixture consisted of 1 cement (Portland 
light) to 1.6 sand to 1.5 crushed stone aggregate (grade lb, nominal 
diameter of ~-inch) to 0.46 water by weight. 
The random wire reinforced concrete was of the same pro-
portions as the plain concrete with the addition of 1.5% by volume 
of one-inch long 26 gage steel wire. The optimum percentage by volume 
-4-
·-
and length of wire for ductility was determined in previous tests 
by Carson and Chen [6]. 
Testing Procedure 
The loading punches were made of tool steel l-inch thick. 
Before the specimens with ducts were loaded, snug fitted steel rods 
were inserted into each end. The length of the rods was such that 
the two rods did not make contact with each other, therefore, they 
could not carry any of the compressive load. The testing was per-
formed on a 120 kip capacity Tinus-Olson Testing Machine. A spherical 
seat was placed on top of the top punch with the bottom punch resting 
on the steel bed of the testing machine •. The load was applied at the 
approximate rate of 1 kip every 10 seconds continuously until failure. 
The control tests were performed on 12-inch standard con-
crete cylinders. Both compression tests and splitting tension 
(indirect tensile) tests were performed on cylinders having the same 
age as the test specimens. 
3. COMPUTING THE BEARING CAPACITY 
From the standard compression test, f' was 7.29 ksi and 
c 
7.45 ksi for plain and random wire reinforced concrete, respectively. 
The average direct tensile strength f~ was estimated to be 80% of the 
result of the splitting tensile test, the resulting f' was 0.45 ksi 
t 
and 0.60 ksi for the plain and random wire. reinforced concrete, re-
spectively. 
-5-
·.The values of upper bound on the average bearing pressure, 
which are tabulated in Table 1, Column 9; were obtained directly from 
Chen and Covarrubias [1] with f~ set equal to 15 f~ and 12 f~ for plain 
and random wire reinforced concrete, respectively. The angle of friction, 
~' used was 20 degrees. Approximate solutions, as given in Ref. 1, were 
used for the case of e/b = 0.5 with ducts. 
To obtain the values of lower bound on the average bearing 
pressure (or an elastic limit solution), the modified Mohr-Coulomb 
criterion (Fig. 3) was used as the yield (or failure) criterion. The 
mQdified Mohr-Coulomb criterion.is constructed using f', f', and~ of 
c t 
the concrete. If the state of stress at any point in the specimen does 
·not violate the yield (or failure) criterion, then the pressure imposed 
can be carried by the blocks [8]. The stresses for the circular cylinder 
with a concentric loading were obtained directly from the elastic solu-
tion given in Ref. 3 with Poisson's ratio of 0.16. 
Since an elastic solution is not known for the other cases, 
a lower bound solution is calculated by assuming an equilibrium stress 
distribution. The assumed stress distributions are shown in Fig. 4. 
Figure 4a assumes that only a circular cylinder with a radius of b-e · 
and a concentric loading has a stress field given by the elastic solu-
tion in Ref. 3, the remainder of the specimen has zero stresses. 
Figure 4b assumes uniform vertical stresses, f', directly under the 
c 
loading punch (excluding the cable duct part) with all other stresses 
equal to zero. Since the conditions described in Figs. 4a and 4b 
satisfy equilibrium and stress boundary conditions and nowhere exceeds 
the Mohr-Coulomb criterion, they give a lower bound solution. 
-6-
The lower bound solutions for square specimens loaded with 
square punches are obtained by assuming that the load from the square 
punches is distributed over the area of a circle with a diameter 
equal to a side of the punch. 
4. RESULTS 
All test results are summarized in Tables 1 and 2. Table 1 
gives the results for the bearing capacity of circular punches on 
circular blocks, and Table 2 contains the results for the square 
punches on square blocks. The concrete properties are given in 
Columns 1, 2, and 3. The geometrical data of the punches and speci-
mens are in Columns 4, 5, and 6. The ratio of the bearing stress q 
to the ultimate compressive stress f' is given in Columns 8, 9, and 
c 
10. The number of specimens tested is given in Column 7 and the 
coefficient of variation in percent is in Column 11. 
The test data indicate that with greater eccentricity the 
greater the divergence between the test results and the calculated 
. upper bounds. This is caused by loss of lateral confinement of the 
bearing area which reduces plastic flowo 
Figure 5 is a non-dimensional plot of the bearing capacity 
of circular punches on circular blocks with"concentric ducts. The 
plot shows excellent agreement with the predicted upper bound. 
The greater ductility of the random wire reinforced con-
crete allowed greater plastic flow to occur and, hence, had 
-7-
resulted closer to the upper bound solution then those obtained for 
plain concrete. 
The square specimens had relatively lower results than 
the corresponding circular specimens. This may be explained by 
the high stress concentrations near the corners of the punch and 
also in the corners of the ducts. These stress concentrations could 
induce premature cracks and hence lower load capacities. Typical 
failures are shown in Figs. 6 and 7. 
5. CONCLUSIONS 
1. The test data were bounded by the calculated upper 
bounds (plastic solution) and lower bounds (elastic 
solution). 
2. The more ductile random wire reinforced concrete 
gave results closer to the calculated upper bounds 
than the plain concrete. 
3. The highly confined concrete gave results which ap-
proximated the calculated upper bounds. 
4. Duct diameters up to about 60% of the punch diameters 
had·little effect on the total bearing capacity of the 
specimens. 
-8-
6. REFERENCES 
1. Chen, W. F. and Covarrubias, S. 
BEARING CAPACITY OF CONCRETE BLOCKS, Journal of Engineering 
Mechanics Division, ASCE, 1971. To appear. 
2. Iyengar, K. T. S. and Yogananda, C. v. 
A THREE-DIMENSIONAL STRESS DISTRIBUTION PROBLEM IN THE AN-
CHORAGE ZONE OF A POST-TENSIONED CONCRETE BEAM, Magazine 
of Concrete Research, Vol. 18, No. 55, June 1966, pp. 75-84. 
3. Nishibayashi, S., Kiyama, H., and Sakata, K. 
THEORETICAL STUDIES ON THE BEHAVIOR OF CONCRETE UNDER BEAR-
ING PRESSURE, Reports of the Faculty of Engineering, Tottori 
University, Japan, Vol. 1, No. 1, December 1970, pp. 56-63. 
4. Iyengar, K. T. S. and Prabhakara, M. K. 
ANCHOR ZONE STRESSES IN PRESTRESSED CONCRETE BEAMS, Journal 
of the Structural Division, ASCE, Vol. 97, No. ST3, March 
1971, pp. 807-824. 
5. Chen, W. F. and Drucker, D. C. 
BEARING CAPACITY OF CONCRETE BLOCKS OR ROCK, Journal of the 
Engineering Mechanics Division, ASCE, Vol. 95, No. EM4, Proc. 
Paper 6742, August 1969, pp. 955-978. 
6. Carson, J. L. and Chen, W. F. 
STRESS-STRAIN RELATIONS FOR RANDOM WIRE REINFORCED CONCRETE, 
Fritz Engineering Laboratory Report No. 370.1, Lehigh Uni-
versity, Bethlehem, Pennsylvania, October 1970. 
7. Carson, J. L. and Chen, W. F. 
BEARING CAPACITY OF RANDOM WIRE REINFORCED CONCRETE BLOCKS, 
Fritz Engineering Laboratory Report No. 370.4, Lehigh Uni-
versity, Bethlehem, Pennsylvania, December 1970. 
8. Chen, W. F. 
EXTENSIBILITY OF CONCRETE AND THEOREMS OF LIMIT ANALYSIS, 
Journal of the Engineering Mechanics Division, ASCE, Vol. 96, 
No. EM3, Proc. Paper 7369, June 1970, pp. 341-352. 
-9-
(1) (2) (3) 
Concrete f' f I 
(kii) (kfi) Mix 
s:: 
..-1 
CIS 
..-l 
P-4 7.29 .46 
"0 
~ 
0 
1-l 
0 
1.1-1 
s:: 
..-1 
~ 
ex: 7.45 .60 ~ 
1-l 
..-1 
:::t 
a 
0 
"0 
s:: 
CIS 
ex: 
* or Elastic Solution 
TABLE 1 
BEARING CAPACITY OF CIRCULAR PUNCH 
ON CIRCULAR BLOCKS 
(4) (5) (6) (7) (8) (9) (10) 
q/f' 
c 
I * h e c No. of Upper 1 Lower 
- Tests l Test 2a i b a Bound l Bound 
0 3 2.41 2.74 1.67 
.25 0 3 1.78 2.73 1.14 
.so 3 1.20 2.65 1.00 
.75 3 0.93 2.50 1.00 
.167 6 2.26 2.69 0.97 
0 .333 3 2.21 2.58 0.89 
.583 6 2.16 2.17 0.66 
.833 2 1.19 1.55 0.31 
4 .167 3 1.01 1.87 0.97 
.5 .333 2 1.51 1. 73 0.89 
.583 3 1.04 1.39 0.66 
.833 1 0.59 0.86 0.31 
0 3 3.11 3.47 1.92 
·6 .25 0 3 2.20 3.44 1.51 
.so 2 1.74 3.38 1.15 
.75 2 1.24 3.16 1.00 
0 2 2.74 3.19 1.70 
.25 0 3 2.17 3.11 1.48 
.50 3 1.69 2.97 1.00 
.75 3 1.48 2.70 1.00 
.167 2 3.16 3.17 0.97 
4 0 .333 3 2.95 3.05 0.89 
.583 3 2.65 2.63 0.66 
.833 2 . 1.86 1.92 0.31 
.167 1 1.47 2.14 0.97 
, 
.5 .333 1.44 2 1.99 0.89 
.583 1 1.11 1.62 0.66 
.833 2 0.80 1.04 0.31 
-10-
(11) 
Coef. of 
Variation I 
Percent 
11.3 
12.9 
1.3 
3.6 
8.9 
I 4.9 
15.6 I 
6.9 
-I 0.3 
o.s 
19.1 
--
3.9 
5.6 
1.6 
2.2 
1.0 
5.7 
9.5 
2.6 
I 4.4 . 3.6 
I 6.2 10.4 
--
5.9 
--
9.4 
•' 
(1) (2) (3) 
f' Concrete f' c t 
Mix (ksi) (ksi) 
. 
~ 
~ 
ell 
..-I 7.29 .46 p.. 
GI"' 1-1 G) ~ 0 
::: 1-1 
s 0 
o4-1 
"0 ~ ~~ 7.4S .60 ell G) ~~ 
* or Elastic Solution 
TABLE 2 
BEARING CAPACITY OF SQUARE PUNCH 
ON SQUARE BLOCKS 
(4) (S) (6) (7) (8) (9) 
q/f' 
. c 
h e c No. of Upper 
- Test 2a b a Tests Bound 
0 s 2.27 2.74 
.2S 0 s 1. 72 2.SS 
.so 3 1.2S 2.36 
.7S 3 1.24 2.0S 
4 
.167 3 1.78 2.69 
0 .333 3 1. 79 2.S8 
.S83 3 1.66 2.17 
.833 3 1.12 l.SS 
0 3 2.20 3.47 
6 .2S 0 3' 1.93 3.19 
.so 3 l.S4 2.93 
.7S 3 1.27 2.48 
0 2 
.. 
-2.32 3.20 
.2S 0 2 1.92 2.96 
.so 2 1.67 2. 72 
.7S 3 1.42 2.3S 
.167 2 2.Sl 3 .lS 
4 0 .333 2 2.1S 3.01. 
.S83 2 1.89 2.60 
.833 2 1.46 1.88 
-11-
(10) (11) 
* 
Coef. of 
Lower Variation 
Bound Percent 
1.31 S.3 
1.00 6.0 
1.00 9.0 
1.00 8.2 
0. 97 S.4 
0.89 9.1 
0.66 13.3 
0.31 0.9 
l.Sl 4.3 
1.19 9.2 
1.00 S.2 
1.00 4.3 
1.33 3.S 
1.16 4.2 
1.00 3.0 
1.00 S.7 
0.97 6.1 
0.89 4.9 
0.66 7.8 
0.31 3.7 
Cable 
Duct 
Concentric Duct 
(a) 
Cable 
Duct 
Eccentric Duct 
(b) 
Fig. 1: Simplified Problem of the End Bearing in a Post-Tensioned 
Concrete Beam 
STRESS 
I 
I 
/Linear Elastic 
I / 1E:tic-:f:ly Plastic 
I Fracture 
STRAIN 
Fig. 2• Stress-Strain Curve for Concrete and Its Idealization 
I . 
..... 
·w 
I 
.. 
/ 
/ 
,.., 
/ 
I 
I 
I 
I 
I 
\ COMPRESSION 
\ 
\ 
\ 
' \ 
' ', 
.............. 
I 
I 
\ 
\ 
........ --
// 
/ 
I 
\ 
' 
' ......... ......... 
---
........... _________ _.....,. 
f~ 
T 
TENSION 
Fig. 3: Modified Mohr-Coulomb Criterion for Yielding and for Fracture 
I 
..... 
.p. 
I 
I . I E ast1c 1 
Solution 1 
h I 
I 
I 
-Q-o 
.h 
(a) (b) 
Fig. 4: Stress Fields for Lower Bound Solutions 
I 
....... 
V1 
I 
' 
q 
f~ 
5 
4 
0 
--- Wire Reinforced 
-~ Plain Concrete 
o Wire Reinforced Data 
• Plain Cone rete Data 
-- - -o--- - c/J = 20° .,. ____ __ 
!~-----------------~ ----- f~lfi = 12 -o- ................. 
......... 
• • 
0.2 0.4 
c 
a 
0.6 
Fig. 5: Circular Blocks with Concentric Ducts 
,· 
......... ......... 
..........~ 
• 
0.8 
·-
Fig. 5: Typical Failures of Specimens with Ducts 
-16-
·. 
Fig. 6: Typical Failures of Specimens without Ducts 
-17-


Bearing strength of concrete blocks, May 1971, Special Topics report for M. S. degree for Siciliano

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Bearing strength of concrete blocks, May 1971, Special Topics report for M. S. degree for Siciliano

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