Structural Analysis, SI Edition
6th Edition
ISBN: 9780357030981
Author: Aslam Kassimali
Publisher: Cengage Learning US
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Chapter 13, Problem 7P
To determine
Find the reactions and sketch the shear and bending moment diagrams for the given beam using method of consistent deformation.
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Problem 1
=
=
= 13,600
Manometers can be used in combination with cardiovascular catheters to measure blood
pressure based on height differences. In the example in Figure 1, the manometer
contains two fluids: water (density p 995 Kg/m³) and mercury (density pm
Kg/m³). The density of blood is p 1,060 Kg/m³. Assume that there is atmospheric
pressure at the interface between mercury and air. The interface between mercury and
water is at z₁ = 7 cm, the interface between water and blood is at Z2 27 cm, and the
tip of the manometer at za 10 cm.
Recall that the fluid statics equation is dp/dz-pg 0, when the z axis is taken
pointing downwards.
a. What is the gauge pressure po at the interface with air, in mmHg? (5 points)
b. Calculate the gauge pressure ps at the tip of the manometer, in mmHg. (5
points)
N
Z37
blood
ப
Zz
Water
Mercury
Zo
3=0
z
Figure 1. Manometer for blood pressure measurement.
Determine the following for the beam with unknown loading, using
the Shear and Bending Diagrams provided in the figures on the right:
a. The maximum shear stress experienced by the beam.
b. The maximum flexural stress experienced by the beam (Indicate if
this is tensile or compressive flexural stress)
c. The loading diagram (Indicate the magnitudes of the loading/s. The
loads are acting along the plane of symmetry of the section)
20 80 20
十十
SHEAR DIAGRAM
x=577.3502692 mm
20 KN
1°
5/3 KN
2°
C
2°
D
A
B
CROSS SECTION
Dimensions are in mm
LOADING DIAGRAM
?
120
40
40
A
B
C
D
1000mm
2000mm
1000mm
-55/3 KN
MB'
C
D
BENDING DIAGRAM
MB
A
B
Σ
Mc
Find the maximum bending stress in ksi for this beam if it is made from a W16x50 steel shape. If the steel yields
at 50 ksi, will the beam support the loads shown without permanently deforming? Confirm the max moment in
the beam by drawing the shear and moment diagram.
18 kip-ft
2 kip/ft
9 ft
Chapter 13 Solutions
Structural Analysis, SI Edition
Ch. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10P
Ch. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - Prob. 17PCh. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - Prob. 20PCh. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61P
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