Chapter 7, Problem 7.32P

Both Fouriers law of heat conduction and ficks law of mass diffusion can be expressed as Q=-kA(dT/dx). What do the quantities Q, k, a and T represent in  a) heat conduction b)mass diffusion

(9) Figure Q9 shows a 2 m long symmetric I beam where the upper and lower sections are 2X wide and the middle section is X wide, where X is 31 mm. The I beam sections are all Y=33 mm in depth. The beam is loaded in the middle with a load of Z=39 kN causing reaction forces at either end of the beam's supports. What is the maximum (positive) bending stress experienced in the beam in terms of mega-Pascals? State your answer to the nearest whole number. Y mm Y mm Y mm Xmm 2X mm Figure Q9 Z KN 2 m

(5) Figure Q5 shows a beam which rests on two pivots at positions A and C (as illustrated below). The beam is loaded with a UDL of 100 kN/m spanning from position B and ending at position D (as illustrated). The start location of B is Y=1.2 m from A. The total span of the UDL is twice the length of Z, where Z=2.2 m. What is the bending moment value at position X=2.5 m, (using the convention given to you in the module's formula book). State your answer in terms of kilo-Newton-metres to 1 decimal place. Bending Moment Value? UDL = 100 kN/m A Ym X = ? B Zm Figure Q5 C * Zm D

You are required to state your answer in millimetres to the nearest whole number. 30 mm 30 mm A. No Valid Answer B. 27 ○ C. 26 O D.33 ○ E. 34 30 mm 50 mm Figure Q14 1m

A beam supports a uniform load and an axial load P = 30 kips. If the maximum allowable tensile stress in the beam is 24 ksi and a maximum allowable compressive stress is 20 ksi, what uniform load can the beam support? Assume P passes through the centroid of the section.

Bending Moment Value? 40 kN 100 kN 100 kN 100 kN 40 kN A B C D E Ym Zm Zm Ym X = ?

(4) Figure Q4 shows a symmetrically loaded beam. The beam is loaded at position A (x = 0 m) and the end of the beam at position E with 30 kN. There is an additional load of 101 kN both at position B (Y = 0.87 m), in the middle at C and at position D. The middle section is 2Z, where Z = 0.82 m). Given that the reaction forces at RB and RD both equal 180 kN, calculate the Bending Moment value (using the convention given to you in the module's formula book) at a position of x=2.30m. State your answer in terms of kilo-Newton-metres to one decimal place. Bending Moment Value? 40 kN 100 kN 100 kN 100 kN 40 kN B D E Ym Zm Zm Ym X = ? Figure Q4

(8) Figure Q8 shows a T cross-section of a T beam which is constructed from three metal plates each having a width of 12 mm and sectional engths of X=72 mm, Y=65 mm and Z=88 mm, where the plates are used for the web section, and the two flange sections respectively, as llustrated in Figure Q8. Calculate the neutral axis of the T-beam cross-section (as measured from the base) in units of millimetres, stating your answer to the nearest 1 decimal place. Z mm Y mm 12 mm X mm Figure Q8 12 mm 12 mm

(10) A regular cross-section XXY mm beam, where X-94 m and Y=62 m and 1800 mm long, is loaded from above in the middle with a load of Z=2 kN causing a compressive Bending Stress at the top of the beam and tensile Bending Stress at the bottom of the beam. The beam in addition experiences a tensile end loading in order to reduce the compressive stress in the beam to a near zero value. The configuration of the beam is illustrated in Figure Q10. Calculate the end loading force required in order to reduce total compressive stress experienced in the beam to be near zero? State your answer to the nearest 1 decimal place in terms of kilo-Newtons. Z kN Y mm 1800 mm X mm ? KN Figure Q10 ? KN