Each problem worth a MAXIMUM of 0.5 percentage points toward TOTAL grade.
Show all work to receive credit. Use previous assignments, class examples, and midterm exam as
reference for completing these problems. Be careful with units!
Problem 1.1
A beam having the properties shown below is subjected to a uniform load.
� 18ft
� 12 in
� 22 in
‘�&
4000 psi
The beam is simply supported at each end. Calculate the required reinforcing if the maximum moment is
250 kip-ft.
Problem 1.2
What factored uniformly distributed load, qu would result in the design moment from 1.1?
Problem 1.3
For the beam in problem 1.1 calculate minimum reinforcement for the beam.
Problem 1.4
If the beam were reinforced with 3- #6 bars (As = 1.32 in2), calculate maximum uniform (line) load
(kip/ft) that the beam can carry.
Problem 1.5
Use the following tributary width
�
()*+ 10ft
Using the solution from problem 1.4 calculate the maximum distributed live load (psf) that the beam can
carry.
ARCH 312, Reinforced Concrete Design. Spring 2016
Problem 1.6
Use the following shear reinforcement information for the beam:
Bar #3
Spacing 6
Calculate beam shear capacity �� .
Problem 2.1
A column having the properties shown below is subjected to a concentrated axial load. Assume that
bending moment is zero.
� 20 in
ℎ 12 in
‘�&
5000 psi
� 1.5%
Calculate axial capacity ��.
Problem 2.2
Assuming the following unbraced length for the column from 2.1 above.
� 14 ft
Calculate the lowest buckling load (accounting for each column orientation)
Problem 2.3
Assuming the following parameters
�3
1.1
�4
/�& 2
Calculate moment magnification factor
Problem 2.4
Using the results of problem 2.1 and assuming the following
�77 40psf
�87 80psf
Tributary area 20ft X 20ft
Calculate the number of floors that the column can support.
ARCH 312, Reinforced Concrete Design. Spring 2016
Problem 3
Consider a simply supported beam with a cross section shown below. Assume that in flexure bottom bars
are in tension. Use the following:
‘�&
= 4500���
�@ = 60 ���
1) Calculate tensile force T and compression force C
2) Calculate depth of compression block at ultimate moment
3) Calculate beam bending capacity ��.
4) Check if member meets minimum flexural reinforcement criteria.
ARCH 312, Reinforced Concrete Design. Spring 2016
Problem 4
Consider a beam shown below. The beam is supported on neoprene bearings (providing pin supported
condition for both ends) The beams are spaced at 12 ft on center.
‘�&
= 6000���
�@ = 60 ���
1) Calculate moment of inertia of beam section.
2) Calculate modulus of elasticity of concrete
3) Calculate maximum permitted concentrated load on the beam if deflection under total load
cannot exceed L/240
4) Calculate maximum permitted concentrated load if the maximum live load deflection cannot
exceed 1/2 in.
5) The concentrated load is a column being supported by the transfer beam. If the tributary floor
area for the column is 400ft2 and the total load is 100psf calculate the number of floors that this
beam can support.
ARCH 312, Reinforced Concrete Design. Spring 2016
Problem 5
Using the following information about a beam cross section and the strain distribution on the diagram
below
� = 12in
� = 28��
‘�&
=4000 psi
If the depth of the compression block � = 4��
1) Find the location of neutral axis (dimension c)
2) Find the amount of tension steel area �L required for this beam to be in equilibrium
3) Calculate steel strain and determine if steel yields
Compression
Tension
c
� = 0.003
d
�L
ARCH 312, Reinforced Concrete Design. Spring 2016
Problem 6
Using the data from Problem 3:
1) Calculate nominal concrete shear strength.
2) Assuming the shown shear reinforcement, calculate reinforcement shear strength
3) Calculate total shear capacity of member