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u subscript t t end subscript equals a squared u subscript x x end subscript comma space 0 less or equal than x less or equal than L comma space 0 less than t less than infinity
u left parenthesis 0 comma t right parenthesis equals u left parenthesis L comma t right parenthesis equals 0
u left parenthesis x comma 0 right parenthesis equals sum from n equals 1 to N of B subscript n sin left parenthesis fraction numerator n straight pi straight x over denominator L end fraction right parenthesis comma u subscript t left parenthesis x comma 0 right parenthesis equals sum from n equals 1 to N of A subscript n sin left parenthesis fraction numerator n straight pi straight x over denominator L end fraction right parenthesis

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Calculate the maximum deflection of the following beam in millimetres (mm). Assume the beam is made of steel with E = 200 000 MPa

Please write your answer to 2 decimal places, do not include units in your answer and consider a downwards deflection to be positive.

The formula for the deflection at the tip of a cantilever beam δ = PL3/3EI where a positive deflection here indicates a downwards deflection. 

Image failed to load: Cantilever - 1

 

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У ящик, у якому є 3 кулі, опустили білу кулю,

після чого навмання вийняли одну кулю. Знайдіть імовірність того, що вона біла,

якщо рівноможливі всі припущення про колір перших куль. Відповідь заокругліть до тисячних.

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נתונה הבעיה

u subscript t t end subscript minus u subscript x x end subscript equals 0 space space space space space space space space space space space minus infinity less than x less than infinity comma space space space space minus infinity less than t less than infinity
u left parenthesis x comma 0 right parenthesis equals sin left parenthesis x right parenthesis space space space space space space space space space space space space space minus infinity less than x less than infinity
u subscript t left parenthesis x comma 0 right parenthesis equals fraction numerator 1 over denominator 1 plus x squared end fraction space space space space space space space minus infinity less than x less than infinity

הגל המתקדם שמאלה (גל נסוג) הוא: 

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The beam shown has a yield stress equal to 289MPa.  What is the maximum moment the beam can carry when bending about the xx axis?

Present you answer in units of kNm to one decimal place, but do NOT include the units in your answer

Image failed to load: T-beam

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The beam shown (dimensions in mm) has a yield stress equal to 337MPa.  

Based on using the bending stress formula σ = My/I, what is the maximum moment the beam can carry assuming the beam is bending about the horizontal axis?

Present you answer in units of kNm to one decimal place, and do NOT include any units in your answer

Image failed to load: Rec Beam

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נתונה הבעיה

u subscript t t end subscript minus u subscript x x end subscript equals 0 comma space space space space space space space space 0 less than x less than pi comma space space t greater than 0
u left parenthesis 0 comma t right parenthesis equals 0 comma space space space space space space space space space space space t greater or equal than 0
u left parenthesis pi comma t right parenthesis equals 0 comma space space space space space space space space space space t greater or equal than 0
u left parenthesis x comma 0 right parenthesis equals x comma space space space space space space space space space space 0 less or equal than x less or equal than pi
u subscript t left parenthesis x comma 0 right parenthesis equals 0 comma space space space space space space space space 0 less or equal than x less or equal than pi

ונתון הפתרון למד"ח ותנאי השפה:  u left parenthesis x comma t right parenthesis equals sum from n equals 1 to infinity of open parentheses A subscript n cos left parenthesis n t right parenthesis plus B subscript n sin left parenthesis n t right parenthesis close parentheses sin left parenthesis n x right parenthesis

הפתרון לבעיה  הוא: 

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Where is the exact location of the maximum tension bending stress for the following beam, assuming the BMD is drawn to scale and the cross section is symmetrical?

Remember the positive axis for beam bending is vertically down down and a positive moment equates  to the beam have a sagging/concave deflected shape while a negative moment equates to the beam have a hogging deflected shape.

Image failed to load

 

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For the beam shown, when bending about the horizontal axis and using the bending stress formula σ=My/I, what value of 'y' would you use if you wanted to calculate:

Image failed to load: y value ubeam

Exclude units from your answers

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