This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY
Mechanics of Materials (CE130) Section I College of Engineering The Second Mid—term Examination Problem 1.
Draw shear & moment diagrams for the following beams (see: Fig. 1 (a) and label the peak
values for the corresponding maximum shear and maximum moment. (30 points (15 each)) ' (I) (b) Figure 1‘. Beams with external loads Problem 2. An Ibeam shown in Fig. 2 is made of three planks, which are connected by nails. Suppose that
each nail can sustain a shear force 1000N. Let t 2 50mm and b = 500mm. Suppose that the beam
cross section is subjected to a shear force V = 5kN. Find the maximum nail spacing. _ VQ _ S _ VQ
T ‘ Izt’ q” A ' Iz
Q = / mm = Ag
A
I z = L,c + dgA parallel axis theorem
3
I u = % for rectangular cross section. (1) (20 points) Figure 2: The Ibeam. Problem 3. (A) (I) Figure 3: A T beam: (a) the geometry of the crosssection; (b) the stressstrain relation. Y,v free end Figure 4: A beam with concentrated moment. A Tbeam shown in Fig. 4 (a) with b = 20mm and h = 200mm, which is made of linear
elasticperfectly plastic material (shown in Fig 4 Find: 1. The position of the elastic nuetral axis ?
Find 11 ?;
Find the yield moment, My ? Find the neutral axis position for plastic bending (no elastic core) ? 9"???” Find the ultimate bending moment, Mun ? (30 points) Problem 4. Consider the cantilever beam with span L = a + b. The beam is subjected with a concentrated
moment at the position a: = a in downward direction. The ﬂexural rigidity of the beam is E1 =
const.. (Recommend using singularity function method). d4v(x) E1 (1554 =q(x) (2) (20 points)
(1) What is the q(:t) ? (a)
(b)
(C)
(d)
(e)
(2)
1. State the four boundary conditions; 2. Find the beam deﬂection v(:1:); 3. Find the beam deﬂection at a: = 0. UNIVERSITY OF CALIFORNIA, BERKELEY
Mechanics of Materials (CE130) Section 11 College of Engineering The Second Midterm Examination Problem 1.
Draw shear & moment diagrams for the following beams (see: Fig. 1 (a)(b)) and label the peak
values for the corresponding maximum shear and maximum moment. (30 points (15 each)) qo U2 LIZ
@) Figure 1: Beams with external loads Problem 2. An T—beam shown in Fig. 2 is made of two planks, which are connected by nails. Suppose that
each nail can sustain a shear force 1000N. Let t = 50mm and b = 500mm. Suppose that the beam
cross section is subjected to a shear force V = 5kN. Find the maximum nail spacing. T _ VQ _ S
‘ Lﬁ q—A
Q = / ydA = A2:
A
I, = I u + dZA parallel axis theorem
3
I zc = {ah—2 for rectangular cross section. (1)
(20 points)
I:
t
z t Figure 2: The Tbeam. Stress (MP8)
100 Strain —50 k
W Figure 3: A I beam: (a) the geometry of the crosssection; (b) the stressstrain relation. Y Figure 4: A beam with concentrated force. Problem 3.
A Ibeam shown in Fig. 4 (a) with t = 20mm and b 2 200mm, which is made of linear elastic— perfectly plastic material (shown in Fig 4 Find: 1. The position of the elastic nuetral axis ? 2. Find I z ?; 3. Find the yield moment, My ? 4. Find the neutral axis position for plastic bending (no elastic core) ? 5. Find the ultimate bending moment, Mun ? (30 points) Problem 4.
Consider the cantilever beam with span L = a + b. The beam is subjected with a concentrated load at position :1: = a in downward direction. The ﬂexural rigidity of the beam is E1 = const..
(Recommend using singularity function method).
d4v(:c) _ EI (13:4 —q(a:) (2) 2 (20 points)
(1) What is the q(a:) ? (a) (b) (C) (d) (e)
(2)
1. State the four boundary conditions;
2. Find the beam deﬂection v(a:); 3. Find the beam deﬂection at a: = 0. q(x)=P<za>o?
q(a:)=P<:z:—a>_1?
q(z)==—P<:1:—a>_1?
q(a:) —P<a:—a>_2?
q(:z:) —P<:c—a >1? ...
View
Full
Document
This note was uploaded on 12/01/2011 for the course CE 13972 taught by Professor Chow during the Spring '09 term at University of California, Berkeley.
 Spring '09
 CHOW

Click to edit the document details