Fall 2015 Exam [V CE 3303 — Mechanics of Solids
Stress Transformation — Transformation Equations
The state of stress is given on the element. y
1) Determine the normal stress in the x’ direction if the
element is rotated 30" clockwise from the element
sho
Fall 2015 Exam IV CE 3303 e Mechanics of Solids
Stress Transformation — Transformation Equations
The state of stress is given on the element. y
1) Determine the normal stress in the x’ direction if the
element is rotated 30° clockwise from the element ' '
Fall 2015 Exam l| CE 3303 — Mechanics of Solids
Average Normal, Average Shear Stress, and Factor of Safety
Two links are connected at B where a force is applied.
Their cross—sections are identical with dimensions 2 mm x 3 mm.
Pins at A and C are in double
CE 3303 — Mechanics of Solids Fall 2015
Rigid Body Internal Equilibrium
Exam 1.
The following rigid body was cut at section a-a. The positive internal force directions are indicated on the cut.
The applied forces occur at the centerline ofthe rigid body e
Fall 2015 Exam |I CE 3303 e Mechanics of Solids
Average Normal, Average Shear Stress, and Factor of Safety
Two links are connected at B where a force is applied.
Their cross—sections are identical with dimensions 2 mm x 3 mm.
Pins at A and C are in double
CE 3303 — Mechanics of Solids Fall 2015
Rigid Body Internal Equilibrium
The following rigid body was cut at section 3-3. The positive internal force directions ar
The applied forces occur at the centerline of the rigid body elements.
Section Cut a—a
Exa
Problem 1 (30 pts) For the cross-section shown below, compute (i) the moment of inertia for
uncracked section (Ig) neglecting the reinforcement and the cracking moment Mcr, (ii) the
moment of inertia for uncracked section (Ig) considering the reinforcemen
HW#04 Due Monday 02/11/13
P roblem 1 (20 pts)
ACI Section 10.3.5 specifies the maximum amount o f reinforcement, As,max indirectly by
limiting the stain in the tensile reinforcement at the time o f beam failure. For the cross-sections
shown below, determi
Problem 1 (20 points). For the following beam sections, compute Vn . Use f'c = 4000 psi and
fyt = 40 ksi.
22.5
(1)
(2)
Problem 2 (10 pts). ACI Section 11.4.5.1 sets the maximum spacing of vertical stirrups at d/2.
Explain why.
Problem 3 (10 pts). Is the r
H W#05 D ue M onday 02111113
Problem 1 (20 pts)
Determine the maximum unfactored live load, W L, that can be applied to the simply supported
beam shown below. Use the load factors 1.2 for the dead load and 1.6 for the live load. The
concrete strength,
HW#11 (Optional) (100pts)
For the cross-section of a short column shown below, determine Pn and Mn values for Point 4
indicated in the P-M diagram below. Use f'c = 4 ksi and fy = 60 ksi.
HW#07
Due 02/28/13 Thursday
Problem 1 (20 points). For the flanged sections shown below, (1) Determine the required
tensile reinforcement, As,req to resist the ultimate moment, Mu of 900 k-ft, (2) select the
reinforcing bars (i.e., As,pro) based on As,req
Solutions for Homework #01
Problem 1 (10 pts)
Compute the following material properties for a concrete with the compressive strength ( f c' ) of
4500 psi in accordance with ACI 318-11: the split tensile strength ( f ct ), modulus of rupture ( f r )
and mo
Solutions for Homework #02
Problem 1 (10 pts) A concrete beam shown below was tested to measure the modulus of rupture
( f r ) in accordance with ASTM C78/C78M-10. The beam failed due to cracking at the mid-span.
The maximum load recorded at the time of f
HW#06 Due Tuesday 02/26/2013
Problem 1 (20 pts).
(1) Determine the design flexural strength, M n of the section shown below and (2) determine if
the compression bars would yield or not when the beam fails. Use fc = 4 ksi and fy = 60 ksi.
b = 18 in.
d = 2.
Solutions for Homework#07
Problem 1 (20pts)
For the flanged sections shown below, (1) Determine the required tensile reinforcement, As,req to resist
the ultimate moment, Mu of 900 k-ft, (2) select the reinforcing bars (i.e., As,pro) based on As,req, and (
Solutions for Homework #03
For the cross-sections of a beam shown below, determine the nominal bending strength Mn,
using the rectangular stress block concept discussed today in the class (which is also specified by
ACI 10.2.7). Use the compressive streng
Solutions for Homework#08
Problem 1 (20pts)
Determine the design flexural strength, M n . Use f c' 4= 60 ksi.
=
ksi and f y
5" 5" 5"
4"
30"
23"
4#9
3"
15"
Given:
= 4(1.00) 4.0 in 2
As =
= 4 ksi
f c'
1 =0.85
f y = 60 ksi
b = 15 in
d = 30 3 = 27 in
Solution