60
48
36
24
Vu ( x)

12
0

0

 12
 24
 36
 48
 60

0

5

10

15

20

25

x

10
9
8
7
6 s1 ( x) 5
4
3
2
1
0

0

1

2

3

4

5

6

7

8

9

10

11

12

x

10
9
8
7
6 s2 ( x) 5
4
3
2
1
0

0

1

2

3

4

5

6

7

8

9

10

11

12

x
T.Panayotidi.....10/10/2015

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7-2

Explain why the torsion in the edge beam A-B in Fig. 7-21a is called “equilibrium torsion,” while the torsion in the edge beam A1-B1 in Fig. P7-3 is called
“compatibility torsion.”

If the edge beam A-B in Fig. 7-21c did not resist torsion, the beam would rotate, uninhibited, about its longitudinal axis and fail to resist the action of load P. Essentially, the torsional resistance of the beam is required for equilibrium to be satisfied.
On the contrary, if beam A1-B1 in Fig. P7-3 did not resist torsion, the beam would rotate only slightly before the floor’s weight and superimposed loads would be redistributed to other elements, thereby satisfying equilibrium through the redundancy of the system. The torsion in A1B1 only arises from the need to maintain compatibility of deformations between the ends of the joists and the twisting of the edge beam.

7-3

The two parts of this problem refer to the floor plan shown in Fig. P7-3. Assume that the entire floor system is constructed with normal-weight concrete that has a compressive strength, f’c = 4,500 psi. Also, assume that the longitudinal steel has a yield strength of fy = 60 ksi and that the transverse steel has a yield strength of fyt = 40 ksi.
a)

Design the spandrel beam between columns B1 and C1 for bending, shear, and torsion. Check all of the appropriate ACI Code requirements for strength, minimum reinforcement area, and reinforcement spacing are satisfied. Step 1: