Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 16, Problem 20P
A cylindrical beam carries a compression load
where
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Given the beam shown below, determine the shear force and bending moment at point C. Given the dimensions a = 2 m, b = 5.9 m and c = 2 m, and the load
intensities e = 10 kN/m and f = 2 kN/m.
e kN/m
f kN/m
am
bm
cm
A
B
D
Shear force (observe the up on the left, down on the right positive sign convention):
SFc =
Number
Units
(tolerance 0.2 kN)
Bending moment (observe the sagging positive sign convention):
BMc =
Number
Units
(tolerance 1 kN*m)
3. A solid cement rectangular lentil (beam) with length L = 1.5 m is positioned as shown. The lentil
is fixed supported on its left hand side and simply supported on its right hand side with
y(0) = 0, y'(0) = 0. It is given that for this beam, E I = k. The lentil carries a point load
w(x) = k 60 8(x – 1) N/m at x = 1 m. Use the Laplace transform to calculate an expression for
the deflection of this beam. During your calculations, assume y'"(0) = A and y'(0) = B. Express
%3D
the deflection as a piecewise function in terms of A and B.
LINTEL
LINTEL
The dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C.
What is the reaction force at A? Let a positive reaction force be to the right.
Chapter 16 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 16 - 16.1 Design the optimal cylindrical container...Ch. 16 - 16.2 (a) Design the optimal conical container...Ch. 16 - Design the optimal cylindrical tank with...Ch. 16 - The specific growth rate of a yeast that produces...Ch. 16 - A chemical plant makes three major products on a...Ch. 16 - 16.6 Recently chemical engineers have become...Ch. 16 - 16.7 A mixture of benzene and toluene are to be...Ch. 16 - 16.8 A compound A will be converted into B in a...Ch. 16 - In problem 16.8, only one reactor is used. If two...Ch. 16 - 16.10 For the reaction:
equilibrium can be...
Ch. 16 - A chemical plant requires 106L/day of a solution....Ch. 16 - You must design a triangular open channel to carry...Ch. 16 - 16.13 As an agricultural engineer, you must design...Ch. 16 - 16.14 Find the optimal dimensions for a heated...Ch. 16 - A finite-element model of a cantilever beam...Ch. 16 - 16.16 Suppose that you are asked to design a...Ch. 16 - TheStreeter-Phelps model can be used to compute...Ch. 16 - Prob. 18PCh. 16 - 16.19 The flow in an open channel can be predicted...Ch. 16 - A cylindrical beam carries a compression load...Ch. 16 - The Splash River has a flow rate of 2106m3/d, of...Ch. 16 - 16.22 Determine the beam cross-sectional areas...Ch. 16 - AtotalchargeQ is uniformly distributed around a...Ch. 16 - A system consist softwopower plants that must...Ch. 16 - 16.25 The torque transmitted to an induction motor...Ch. 16 - (a) A computer equipment manufacture rproduces...Ch. 16 - A manufacturer provides specialized microchips....Ch. 16 - 16.28 The total drag on an airfoil can be...Ch. 16 - Mechanical/Aerospace Engineering
16.29 Roller...Ch. 16 - 16.30 An aerospace company is developing a new...Ch. 16 - 16.31 A manufacturing firm produces four types of...Ch. 16 - In a similar fashion to the case study described...Ch. 16 - 16.33 Recent interest in competitive and...
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- Consider the following values in the given beam above: L1=6m L2 = 2 m L3 = 4 m L4=3m L5=2 m L6=1m W1 = 90 kN/m W2 = 30 kN/m P = 50 kN M = 60 kN-m Point E is an internal hinge W1 B L2 L3 2 m E W2 L5 L6 Harrow_forwardFor the beam shown, use only singularity functions. V₁ = 45 lbf/in and V/₂ = 5 in. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 0 1400 lbf Hinge JA B₁ C R₂ R₁ 4 in 4 in 2 in V1 V2 D R₂ + What is the value of the peak moment between points Cand D? The peak moment between points C and Dis Ibf.in.arrow_forwardA uniform beam is simply supported at both ends x = 0 and x = L. Find the shape of the center line of the beam, given the weight per unit Length is w. v(x) = [xª – 4 Lx3 + 6L?x²] 24 EI a. y(x) = [x4 – 2Lx3 + L?x²] 24 EI b. 2AEX1- 2Lx3 + L³x] 24 EI C. v(x) = v(x) = [2x4 -5 Lx3 + 3L?x²] 24 EI d. y(x) = [2x4 - 3L³x3 +3L²x²] е. 24 EIarrow_forward
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- The shape of the beam made of U profile ensures safe loading. Find the length c of the overhangs so that it can move. Of the material Safety stress (ç) emn = 50 N / mm2 for tension and compression conditions, (ob) emn = 80 N / mm2. Support spacing of the beam L = 6 m, cross section its dimensions are a = %D 210 mm, b = 150 mm and wall thickness t = 40 mm. The loading condition is P = 30 kN and qo = 40 kN / m. P B (Kesit)arrow_forwardDetermine the maximum compressive bending stress (o max.comp.x=2.8) for the beam section at distance 2.8 m from A, for the beam loaded in Figure 5.1la1(b), in N/mm2. The cross section of the beam is shown in Figure 5.1a1(a). Given D = 120 mm, t = 15 mm, location of centroid of the cross section = 62.1 mm from x-axis, second moment of area with respect to its centroidal x-axis (Iy) = 7.08 x 106 mm“, a = 0.9 m, b = 0.9 m, and P1 = 20 kN. (Note: Use negative sign "-" to denote compressive stresses) t; D Figure 5.1a1(a) P, kN A В D a m b m 3 m Figure 5.1a1(b)arrow_forwardThe figure below shows the cross-section of an axisymmetric composite beam that comprises steel (Young's modulus 270 GPa) and aluminum (Young's modulus 90 GPa) sections that are bonded together. The steel section is of wall thickness 15 mm and the aluminum section is of wall thickness 10mm. The steel section comprises 4 axisymmetric holes of 5 mm diameter as shown. Given that the beam is bent by a couple moment of 1200 Nm, determine the maximum stress in steel and aluminum. 4 holes of diameter 5 mm. 12 mm steel aluminumarrow_forward
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